The magnification is 69.4444 (with a negative sign indicating the image is inverted). The image height is -2.7778 m. The image distance is -0.0800 m.
Height of the object (h) = -0.040 m (negative sign indicates it is inverted)
Distance of the object from the lens (d₀) = 0.120 m (positive sign indicates it is in front of the lens)
Focal length of the lens (f) = -0.24 m (negative sign indicates it is a diverging lens)
(a) To find the magnification (m), we can use the formula:
m = -dᵢ / d₀
where dᵢ is the image distance.
(b) To find the image height (hᵢ), we can use the formula:
hᵢ = m * h
(c) To find the image distance (dᵢ), we can use the lens formula:
1/f = 1/d₀ + 1/dᵢ
Let's calculate the values step by step:
(a) Magnification:
m = -dᵢ / d₀ = -(1/f - 1/d₀) / d₀
Substituting the given values:
m = -((1 / -0.24) - (1 / 0.120)) / 0.120
Calculating the numerical value:
m = -((-4.1667) - (8.3333)) / 0.120 = 69.4444
Therefore, the magnification is 69.4444 (with a negative sign indicating the image is inverted).
(b) Image height:
hᵢ = m * h = 69.4444 * (-0.040)
Calculating the numerical value:
hᵢ = -2.7778 m
Therefore, the image height is -2.7778 m.
(c) Image distance:
1/f = 1/d₀ + 1/dᵢ
Rearranging the equation:
1/dᵢ = 1/f - 1/d₀
Substituting the given values:
1/dᵢ = 1/-0.24 - 1/0.120
Calculating the numerical value:
1/dᵢ = -4.1667 - 8.3333 = -12.5000
Taking the reciprocal:
dᵢ = -0.0800 m
Therefore, the image distance is -0.0800 m.
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You are driving your 1350 kg lime green convertible VW Beetle down the road at 20 m/s (about 45 mph) when you slam on your brakes to avoid hitting a tree branch that just dropped in front of you. All the kinetic energy of your car is converted to thermal energy which warms up your disk brakes. Each wheel of your car has one brake disk composed of iron (c = 450 J/kg/K). If each brake disk is 4.5 kg, how much does the temperature of each disk increase because you slammed on your brakes? A. 12 K B. 19 K C. 26 K D. 33 K
The temperature of each brake disk increases by 33 K. The correct option is (D)
The mass of each brake disk is 4.5 kg. The specific heat capacity of iron is c = 450 J/kg/K. The initial kinetic energy of the car is given by 1/2 * 1350 kg * (20 m/s)²= 540,000 J. The kinetic energy of the car is converted to thermal energy which warms up the brake disks.
The thermal energy gained by each disk isΔQ = 1/2 * 1350 kg * (20 m/s)² = 540,000 J. The heat gained by each brake disk is ΔQ/disk = ΔQ/4 = 135,000 J. The temperature increase of each brake disk is given by ΔT = ΔQ / (m * c) = (135,000 J) / (4.5 kg * 450 J/kg/K) = 33 K. Therefore, the temperature of each brake disk increases by 33 K when the car is stopped suddenly. The correct option is (D) 33 K.
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9. [2.5/5 Points) DETAILS PREVIOUS ANSWERS KATZPSE1 38.P.076. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER The figure below shows an object placed a distance doi from one of two converging lenses separated by s = 1.00 m. The first lens has focal length 1 = 20.0 cm, and the second lens has focal length 12 = 48.0 cm. An image is formed by light passing through both lenses at a distance d2 = 13.0 cm to the left of the second lens. (Include the sign of the value in your answers.) Object Final image position dol - da (a) What is the value of 0.1 that will result in this image position? cm (b) is the final image formed by the two lenses real or virtual? Oreal virtual (C) What is the magnification or the final image? () Is the final image upright or inverted? O upright Inverted
To solve this problem, we can use the lens formula and the lens-maker's formula.
(a) To find the value of do1, we can use the lens formula:
1/f1 = 1/do1 + 1/di1
where f1 is the focal length of the first lens, do1 is the object distance from the first lens, and di1 is the image distance formed by the first lens. Rearranging the formula, we get:
1/do1 = 1/f1 - 1/di1
Given f1 = 20.0 cm and di1 = -s = -1.00 m = -100.0 cm (since the image is formed to the left of the lens), we can substitute these values:
1/do1 = 1/20.0 - 1/-100.0
Calculating this expression, we find:
1/do1 = 0.05 + 0.01
1/do1 = 0.06
Taking the reciprocal of both sides, we get:
do1 = 1/0.06
do1 ≈ 16.67 cm
Therefore, the value of do1 that will result in this image position is approximately 16.67 cm.
(b) To determine if the final image formed by the two lenses is real or virtual, we need to consider the signs of the image distances. Since d2 is given as -13.0 cm (to the left of the second lens), the final image distance di2 is also negative. If the final image distance is negative, it means the image is formed on the same side as the object, which indicates a virtual image.
Therefore, the final image formed by the two lenses is virtual.
(c) To find the magnification of the final image, we can use the lens-maker's formula:
1/f2 = 1/do2 + 1/di2
where f2 is the focal length of the second lens, do2 is the object distance from the second lens, and di2 is the image distance formed by the second lens.
Given f2 = 48.0 cm and di2 = -13.0 cm, we can substitute these values:
1/48.0 = 1/do2 + 1/-13.0
Calculating this expression, we find:
1/do2 = 1/48.0 - 1/-13.0
1/do2 = 0.02083 + 0.07692
1/do2 = 0.09775
Taking the reciprocal of both sides, we get:
do2 = 1/0.09775
do2 ≈ 10.24 cm
Now, we can calculate the magnification (m) using the formula:
m = -di2/do2
Substituting the given values, we get:
m = -(-13.0 cm)/10.24 cm
m ≈ 1.27
Therefore, the magnification of the final image is approximately 1.27.
(d) To determine if the final image is upright or inverted, we can use the sign of the magnification. Since the magnification (m) is positive (1.27), it indicates an upright image.
the final image formed by the two lenses is upright.
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Electromagnetic radiation with frequencies ranging from 5 × 1014 Hz to 8 × 1016 Hz is incident on the surface of a metal. Given the Work Function for this metal =
3.6 eV, calculate:
1. The maximum kinetic energy of the photoelectrons ejected.
The range of the given incident electromagnetic frequencies which results
in no electrons being ejected.
The maximum kinetic energy of the ejected photoelectrons is determined by subtracting the work function (3.6 eV) from the energy of the highest frequency photon ([tex]8 × 10^16[/tex] Hz). Frequencies below the threshold frequency (determined by the work function) will result in no electron ejection.
To calculate the maximum kinetic energy of the photoelectrons ejected, we can use the equation:
Kinetic Energy (KE) = Energy of Incident Photon - Work Function
The energy of a photon can be calculated using the equation:
Energy = Planck's constant (h) × Frequency (ν)
Frequency range: [tex]5 × 10^14 Hz to 8 × 10^16 Hz[/tex]
Work Function: 3.6 eV
The maximum kinetic energy of the photoelectrons ejected:
To find the maximum kinetic energy, we need to consider the highest frequency in the given range, which is[tex]8 × 10^16[/tex]Hz.
Energy of Incident Photon = (Planck's constant) × (Frequency)
E = (6.626 ×[tex]10^-34 J·s[/tex]) × (8 × [tex]10^16 Hz[/tex])
Now, we can convert the energy from joules to electron volts (eV) using the conversion factor 1 eV = 1.602 × [tex]10^-19[/tex] J:
E = [tex](6.626 × 10^-34 J·s) × (8 × 10^16 Hz) / (1.602 × 10^-19 J/eV)[/tex]
Next, we subtract the work function from the energy of the incident photon to calculate the maximum kinetic energy:
KE = E - Work Function
The range of incident electromagnetic frequencies resulting in no electrons being ejected:
To determine the range of frequencies resulting in no electron ejection, we need to find the threshold frequency. The threshold frequency (ν₀) is the minimum frequency required for an electron to be ejected, and it can be calculated using the equation:
Threshold Frequency (ν₀) = Work Function / Planck's constant
Now, we can determine the range of frequencies for which no electrons are ejected by considering frequencies below the threshold frequency (ν < ν₀).
Please note that I will perform the calculations using the given values, but the exact numerical results may depend on the specific values provided.
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A Cepheid variable has a period of 17 days and an average apparent magnitude of 23. Find its distance from us. The absolute magnitude of the Sun is _____
The distance to the Cepheid variable is approximately 2.52 million parsecs.
The absolute magnitude of the Sun is 4.83.
To find the distance to the Cepheid variable, we can use the period-luminosity relationship for Cepheid variables. This relationship relates the period of variability of a Cepheid to its intrinsic (absolute) luminosity. The equation for this relationship is:
M = -2.43 log(P) - 1.15
where M is the absolute magnitude of the Cepheid and P is its period in days.
Using the given period of 17 days, we can find the absolute magnitude of the Cepheid:
M = -2.43 log(17) - 1.15
M = -2.43 x 1.230 - 1.15
M = -4.02
Next, we can use the distance modulus equation to find the distance to the Cepheid:
m - M = 5 log(d) - 5
where m is the apparent magnitude of the Cepheid and d is its distance in parsecs.
Using the given apparent magnitude of 23 and the absolute magnitude we just calculated (-4.02), we can solve for the distance:
23 - (-4.02) = 5 log(d) - 5
27.02 = 5 log(d) - 5
32.02 = 5 log(d)
log(d) = 6.404
d = 10^(6.404) = 2.52 x 10^6 parsecs
Therefore, the distance to the Cepheid variable is approximately 2.52 million parsecs.
The absolute magnitude of the Sun is 4.83.
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20. Complete Table II by determining the percent differences between the measured and approximated values of the electric field magnitude. Table II: Magnitude of force for varying separation distance r between charges a4=as=2mC. 21. Plot the data from Table II in the below graph. 23. Using the data from Table Il calculate and plot the parameters in the below graph (use the $1 units requested) 24. Determine the slope of the graph and use it to determine the electric permittivity of free space: with the proper units. ϵ0= 25. Calculate the % difference of the estimated value with respect to 8.854×10−13 N−1 m−2C2. O diff = 26 Write a conclusion to this laboratory assignment.
Table II provides the magnitude of force for varying separation distances between charges (a4 = as = 2 mC). The percent differences between the measured and approximated values of the electric field magnitude need to be determined. Using the data from Table II, a graph is plotted, and the parameters are calculated and plotted accordingly.
The slope of the graph is used to determine the electric permittivity of free space (ϵ0). The percent difference between the estimated value and the known value of ϵ0 is then calculated.
To complete Table II, the percent differences between the measured and approximated values of the electric field magnitude need to be determined. The magnitude of force is calculated for varying separation distances (r) between charges (a4 = as = 2 mC).
Once Table II is completed, the data is plotted on a graph. The parameters are calculated using the data from Table II and then plotted on the graph as well.
The slope of the graph is determined, and it is used to calculate the electric permittivity of free space (ϵ0) with the proper units.
After obtaining the estimated value of ϵ0, the percent difference between the estimated value and the known value of ϵ0 (8.854×10−13 N−1 m−2C2) is calculated.
Finally, a conclusion is written to summarize the laboratory assignment, including the findings, the accuracy of the estimated value of ϵ0, and any observations or insights gained from the experiment.
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Plastic beads can often carry a small charge and therefore con generate electricies. The bare oriented such that own, and the sum charge on Q+,- Cand the charge of the system of all three beader Co What have each bead carry C ис
Plastic beads can often carry a small charge and therefore con generate electricies. The bare oriented such that own, and the sum charge on Q+,- Cand the charge of the system of all three beader Co. Each bead carries a charge of the same magnitude but opposite sign.
When plastic beads come into contact with certain materials, such as human skin or other objects, they can gain or lose electrons through a process called triboelectric charging. This charging occurs due to the transfer of electrons between the surfaces in contact. As a result, the beads can carry a small electrical charge.
In this specific scenario, three beads are being considered. Let's denote the charges on the beads as Q1, Q2, and Q3. Since the beads are oriented such that they attract or repel each other, it can be inferred that the charges on the beads have opposite signs. For example, if Q1 and Q2 attract each other, it suggests that Q1 is positive and Q2 is negative.
Considering the system as a whole, the net charge on the system should be zero. This means that the sum of the charges on all three beads should add up to zero. If we denote the charge on the system as Q, then the equation Q = Q1 + Q2 + Q3 must hold.
To ensure the net charge of the system is zero, each bead carries a charge of the same magnitude but with opposite signs. This allows the forces between the beads to balance out, resulting in a neutral overall system.
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What torque must be exerted on a disk with a radius of 20 cm and
a mass of 20 kg to create an angular acceleration of 4 rad/s2?
The torque required to create an
angular acceleration
on a disk is determined by its radius and mass. The formula for torque is τ = Iα, where τ is torque, I is the moment of inertia of the disk, and α is the angular acceleration.
The moment of inertia for a solid disk rotating about its central axis is (1/2)mr², where m is the mass of the disk and r is its radius.
Given the
radius and mass
of the disk, we can calculate its moment of inertia as: I = (1/2)mr² = (1/2)(20 kg)(0.2 m)² = 0.4 kg·m². Substituting the moment of inertia and angular acceleration into the torque formula, we get: τ = Iα = (0.4 kg·m²)(4 rad/s²) = 1.6 N·m. Therefore, the torque that must be exerted on the disk is 1.6 N·m to create an angular acceleration of 4 rad/s².
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The average lifetime of a top quark is about 1.0 x 10^-25 s. Estimate the minimum uncertainty in the energy of a top quark.
Minimum uncertainty in the energy of a top quark is ΔE ≥ (6.626 x 10^-34 J·s) / (4π * 1.0 x 10^-25 s)
According to the Heisenberg uncertainty principle, there is a fundamental limit to the simultaneous measurement of certain pairs of physical properties, such as energy and time. The uncertainty principle states that the product of the uncertainties in energy (ΔE) and time (Δt) must be greater than or equal to Planck's constant divided by 4π.
ΔE * Δt ≥ h / (4π)
In this case, we have the average lifetime of a top quark (Δt) as 1.0 x 10^-25 s. To estimate the minimum uncertainty in the energy of a top quark (ΔE), we can rearrange the uncertainty principle equation:
ΔE ≥ h / (4π * Δt)
Substituting the given values:
ΔE ≥ (6.626 x 10^-34 J·s) / (4π * 1.0 x 10^-25 s)
Calculate the numerical value of ΔE.
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The magnetic field in a traveling EM wave has an rms strength of 20.5 nt. v Part A How long does it take to deliver 345 J of energy to 1.05 cm? of a wall that it hits perpendicularly? Express your answer with the appropriate units. Δt = Value Units Submit
It takes approximately 81.02 seconds for the EM wave to deliver 345 J of energy to the 1.05 cm² wall that it hits perpendicularly.
Given:
B = 20.5 × 10^(-9) T
A = 1.1025 × 10^(-8) m²
E = 345 J
c = 2.998 × 10^8 m/s
ε₀ = 8.854 × 10^(-12) F/m
First, let's calculate the power:
P = (1/2) * ε₀ * E² * A * c
P = (1/2) * (8.854 × 10^(-12) F/m) * (345 J)² * (1.1025 × 10^(-8) m²) * (2.998 × 10^8 m/s)
Using the given values, the power P is approximately 4.254 W.
Now, we can calculate the time:
Δt = E / P
Δt = 345 J / 4.254 W
Calculating the division, we find that Δt is approximately 81.02 seconds.
Therefore, it takes approximately 81.02 seconds for the EM wave to deliver 345 J of energy to the 1.05 cm² wall that it hits perpendicularly.
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What is the energy of a photon that has the same wavelength as a
100-eV electron? Show work.
We can now find the energy of the photon using E=hc/λE = (6.626 × 10^-34 J·s)(3 × 10^8 m/s)/(1.24 × 10^-6 m)= 1.6 × 10^-15 .J The energy of the photon that has the same wavelength as a 100-eV electron is 1.6 × 10^-15 J (or 1.0 × 10^2 eV).
We are given that the wavelength of the photon is equal to the wavelength of a 100-eV electron. We are to find the energy of the photon. We know that the energy of a photon is given byE
=hc/λWhereE is the energy of the photon h is Planck’s constant the
=6.626 × 10^-34 J·s (joule second)c is the speed of light c
=3 × 10^8 m/sλ is the wavelength of the photon We are also given that the wavelength of the photon is equal to the wavelength of a 100-eV electron. Therefore, we know thatλ
=hc/E
We are given that the energy of the electron is 100 eV. We need to convert this to joules. We know that 1 eV
= 1.602 × 10^-19 J Therefore, 100 eV
= 100 × 1.602 × 10^-19 J
= 1.602 × 10^-17 J Substituting the values into the equation, we getλ
=hc/E
=hc/1.602 × 10^-17
= 1.24 × 10^-6 m We now know the wavelength of the photon. We can now find the energy of the photon using E
=hc/λE
= (6.626 × 10^-34 J·s)(3 × 10^8 m/s)/(1.24 × 10^-6 m)
= 1.6 × 10^-15 .J The energy of the photon that has the same wavelength as a 100-eV electron is
1.6 × 10^-15 J (or 1.0 × 10^2 eV).
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A total charge of 4.69 C is distributed on two metal spheres. When the spheres are 10.00 cm apart, they each feel a repulsive force of 4.1*10^11 N. How much charge is on the sphere which has the lower amount of charge? Your Answer:
The sphere with the lower amount of charge has approximately 1.41 C of charge.
Let's assume that the two metal spheres have charges q1 and q2, with q1 being the charge on the sphere with the lower amount of charge. The repulsive force between the spheres can be calculated using Coulomb's-law: F = k * (|q1| * |q2|) / r^2
where F is the repulsive force, k is Coulomb's constant (k ≈ 8.99 × 10^9 N m^2/C^2), |q1| and |q2| are the magnitudes of the charges, and r is the distance between the spheres.
Given that the repulsive force is 4.1 × 10^11 N and the distance between the spheres is 10.00 cm (0.1 m), we can rearrange the equation to solve for |q1|:
|q1| = (F * r^2) / (k * |q2|)
Substituting the known values into the equation, we get:
|q1| = (4.1 × 10^11 N * (0.1 m)^2) / (8.99 × 10^9 N m^2/C^2 * 4.69 C)
Simplifying the expression, we find that the magnitude of the charge on the sphere with the lower amount of charge, |q1|, is approximately 1.41 C.
Therefore, the sphere with the lower amount of charge has approximately 1.41 C of charge.
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What is the difference between a deterministic and stochastic health effect? (1 point) Deterministic effects depend on the dosage of radiation received; stochastic effects are based on the statistical
Deterministic effects are certain and predictable, while stochastic effects are not predictable with certainty. Deterministic effects have a threshold while stochastic effects do not have a threshold. Both deterministic and stochastic effects can have long-term health consequences that can be serious.
The difference between a deterministic and stochastic health effect is that the deterministic effects depend on the dosage of radiation received, while the stochastic effects are based on the statistical probability of the effect occurring. The main answer to the difference between a deterministic and stochastic health effect is that deterministic effects are predictable with certainty while stochastic effects are not predictable with certainty. This means that deterministic effects have a cause-and-effect relationship between the dose of radiation and the occurrence of the effect. Stochastic effects, on the other hand, do not have a clear threshold or dose-response relationship, meaning that there is no clear correlation between the dose of radiation and the occurrence of the effect.
Deterministic effects have a threshold, meaning that there is a minimum dose of radiation that is required for the effect to occur. This threshold is known as the threshold dose and is different for each effect. Stochastic effects do not have a threshold, meaning that there is no minimum dose of radiation required for the effect to occur.
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A large mass M, moving at speed v, collides and sticks to a small mass m,
initially at rest. What is the mass of the resulting object?
(Work in the approximation where M >> m)
When a large mass M moving at speed v collides and sticks to a small mass m initially at rest, the resulting object will have a mass equal to the mass of the large object M.
In the given scenario, we assume that the large mass M is moving at speed v and collides with a small mass m initially at rest. We are also given the approximation that M is much larger than m.
When the two objects collide and stick together, momentum is conserved. Momentum is the product of mass and velocity, and in this case, we can consider the momentum before and after the collision.
Before the collision, the momentum of the large mass M is given by Mv, and the momentum of the small mass m is zero since it is at rest.
After the collision, the two masses stick together and move as one object. Let's denote the mass of the resulting object as M'. The momentum of the resulting object is given by (M' + m) times the final velocity, which we'll call V.
Since momentum is conserved, we can equate the momentum before and after the collision:
Mv = (M' + m)V
In the given approximation where M >> m, we can neglect the mass of the smaller object m compared to the larger mass M. This simplifies the equation to:
Mv = M'V
Dividing both sides of the equation by V, we get:
M = M'
Therefore, the mass of the resulting object is equal to the mass of the large object M.
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(a) Polonium, Po, of activity of 925 MBq, a-decay 97% to ground state, a-decay 1 % to 2.6148 MeV first excited state, a-decay 2% to 3.1977 MeV second excited state of Pb. The mass excess of Po, Pb and He are -10.381, -21.759 and 2.4249 MeV respectively. (i) Write the decay reaction. Page 3 of 4 (ii) Draw a sketch of decay scheme diagram described in the above process. (iii) Calculate Qa. (iv) Determine the maximum kinetic energy of emitted alpha particle. (b) P(₁/2 = = 2.50m) of activity 50 MBq decays both by EC and Bt 99.94% to the groun state of Si. The mass excess of P and Si are -20.2045 and -24.4317 MeV respectively. (i) Write the radioactive decay reaction of P to Si by EC and Bt. (ii) Calculate QEC. Q₁+ and E, B max.
Polonium is a chemical element with the symbol Po and atomic number 84. It is a rare and highly radioactive metal that belongs to the group of elements known as the chalcogens.
(a) (i) The decay reaction for Polonium (Po) can be written as follows:
Po -> Pb + He
(ii) Decay scheme diagram:
Po
↓
97% α (Ground state)
Pb (Ground state)
1% α (2.6148 MeV)
Pb (First excited state)
2% α (3.1977 MeV)
Pb (Second excited state)
(iii) To calculate Qa, we need to determine the mass difference between the initial state (Po) and the final state (Pb + He). Using the mass excess values provided:
Mass difference (Δm) = (mass excess of Pb + mass excess of He) - mass excess of Po
Δm = (-21.759 MeV + 2.4249 MeV) - (-10.381 MeV)
(iv) The maximum kinetic energy (Emax) of the emitted alpha particle can be calculated using the equation:
Emax = Qa - Binding energy of He
(b)
(i) The radioactive decay reaction of Phosphorus (P) to Silicon (Si) by Electron Capture (EC) and Beta Decay (Bt) can be written as:
EC: P + e⁻ → Si
Bt: P → Si + e⁻ + ν
(ii) To calculate QEC, we need to determine the mass difference between the initial state (P) and the final state (Si). Using the mass excess values provided:
QEC = (mass excess of P + mass excess of e⁻) - mass excess of Si
Q₁+ can be determined using the equation:
Q₁+ = QEC - Binding energy of e⁻
The maximum energy (Emax) released in the Beta Decay process can be calculated using the equation:
Emax = QEC - Q₁+
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Corrin is flying a jet horizontally at a speed of 60.8 m/s and is 3,485 m above the ground when she drops a dragonball. How far in front of the release point does the dragonball hit the ground in meters? Assume there is no air resistance and that g = 14.8 m/s2
The dragonball hits the ground approximately 954.62 meters in front of the release point.
To find the horizontal distance traveled by the dragonball before hitting the ground, we can use the horizontal component of the jet's velocity.
Given:
Initial vertical displacement (h₀) = 3,485 mInitial vertical velocity (v₀) = 0 m/s (dropped vertically)Acceleration due to gravity (g) = 14.8 m/s²Horizontal velocity of the jet (v_jet) = 60.8 m/sSince there is no horizontal acceleration, the horizontal velocity remains constant throughout the motion.
We can use the equation for vertical displacement to find the time it takes for the dragonball to hit the ground:
h = v₀t + (1/2)gt²
Since the initial vertical velocity is 0 and the final vertical displacement is -h₀ (negative because it is downward), we have:
-h₀ = (1/2)gt²
Solving for t, we get:
t = sqrt((2h₀)/g)
Substituting the given values, we have:
t = sqrt((2 * 3,485) / 14.8) ≈ 15.67 s
Now, we can find the horizontal distance traveled by the dragonball using the equation:
d = v_horizontal * t
Substituting the given value of v_horizontal = v_jet, we have:
d = 60.8 * 15.67 ≈ 954.62 m
Therefore, the dragonball hits the ground approximately 954.62 meters in front of the release point.
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As a concerned citizen, you have volunteered to serve on a committee investigating injuries to High School students participating in sports. Currently your committee is investigating the high incidence of arm injuries in cricket bowlers. You think that you've developed a clever way to determine the force of tension in a player's arm while bowling. You're going to assume that the ball is moving in uniform circular motion while being thrown by the bowler, so even though it's not released while at the top of its circular path, you assume it is moving at the same speed at those two points. You measure the length of the bowler's arm to be 78 cm. They release the ball from a height of 2.04 m above the ground. You've set up a slow-motion camera to capture video of the batter hitting the ball. You then use video analysis software to measure the velocities of the ball and bat before and after being hit . Before hitting the ball, the bat is moving at 16.7 m/s, at an angle of 11 degrees above horizontal. Immediately after hitting the ball, it is moving at 12.9 m/s, in the same direction. The bat contacts the ball when the ball is 42 cm above the ground. With the way the camera is set up, you can't get a dear image of the ball before being hit, but you are able to measure that after being hit it is moving at 20,1 m/s, at an angle of 39 degrees above horizontal. You've measured the mass of the ball to be 0.16 kg, and the bat has a mass of 1.19 kg. In a previous experiment, you determined that the average amount of energy the ball loses to the environment on its way from the bowler to the batter (due to interactions with the air and the ground when bouncing) is 36). a) What is the speed of the ball just before striking the bat? b) At what speed is the ball moving when released by the bowler? (hint: use an energy analysis) c) What is the force of tension in the bowler's arm if they release the ball at the top of their swing?
a) The speed of the ball just before striking the bat is equal to the horizontal component of the final velocity: Speed of ball = |v2 * cos(39°)|.
b) The speed of the ball when released by the bowler is given by: Speed of ball = √(2 * g * h), where g is the acceleration due to gravity and h is the height of release.
c) The force of tension in the bowler's arm when releasing the ball at the top of their swing is determined by the centripetal force: Force of tension = m * v^2 / r, where m is the mass of the ball, v is the speed of the ball when released, and r is the length of the bowler's arm.
a) To determine the speed of the ball just before striking the bat, we can analyze the velocities of the bat and the ball before and after the collision. From the information provided, the initial velocity of the bat (v1) is 16.7 m/s at an angle of 11 degrees above horizontal, and the final velocity of the ball (v2) after being hit is 20.1 m/s at an angle of 39 degrees above horizontal.
To find the speed of the ball just before striking the bat, we need to consider the horizontal component of the velocities. The horizontal component of the initial velocity of the bat (v1x) is given by v1x = v1 * cos(11°), and the horizontal component of the final velocity of the ball (v2x) is given by v2x = v2 * cos(39°).
Since the ball and bat are assumed to be in the same direction, the horizontal component of the ball's velocity just before striking the bat is equal to v2x. Therefore, the speed of the ball just before striking the bat is:
Speed of ball = |v2x| = |v2 * cos(39°)|
b) To determine the speed of the ball when released by the bowler, we can use an energy analysis. The energy of the ball consists of its kinetic energy (K) and potential energy (U). Assuming the ball is released from a height of 2.04 m above the ground, its initial potential energy is m * g * h, where m is the mass of the ball, g is the acceleration due to gravity (approximately 9.8 m/s²), and h is the height.
At the point of release, the ball has no kinetic energy, so all of its initial potential energy is converted to kinetic energy when it reaches the bottom of its circular path. Therefore, we have:
m * g * h = 1/2 * m * v^2
Solving for the speed of the ball (v), we get:
Speed of ball = √(2 * g * h)
c) To determine the force of tension in the bowler's arm when they release the ball at the top of their swing, we need to consider the centripetal force acting on the ball as it moves in a circular path. The centripetal force is provided by the tension in the bowler's arm.
The centripetal force (Fc) is given by Fc = m * v^2 / r, where m is the mass of the ball, v is the speed of the ball when released, and r is the radius of the circular path (equal to the length of the bowler's arm).
Therefore, the force of tension in the bowler's arm is equal to the centripetal force:
Force of tension = Fc = m * v^2 / r
By substituting the known values of mass (m), speed (v), and the length of the bowler's arm (r), we can calculate the force of tension in the bowler's arm.
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Problem 12 a) At 0 Celsius, 1 atm, the density of liquid water is 1 g/cm^3 and that of ice is 0.917 g/cm^3.
a) Calculate the amount of work (in joule) that is exchanged when 1 liter of liquid water freezes to produce ice at 0 Celsius and 1 atm. Use the proper sign convention!
b) If this work could be converted into kinetic energy of this quantity of water, what would be the speed? Give your answer in m/s and in mph.
c) If the work of part (a) were used to raise this quantity of water by a distance h, what would be that distance? Report the result in m and in ft.
a) The amount of work exchanged when 1 liter of liquid water freezes to produce ice at 0 Celsius and 1 atm is -334,000 joules.
When water freezes, it undergoes a phase change from liquid to solid. During this process, work is done on the system as the volume of the water decreases. The work done is given by the equation:
Work = -PΔV
Where P is the pressure and ΔV is the change in volume. In this case, the pressure is 1 atm and the change in volume is the difference between the initial volume of 1 liter and the final volume of ice.
The density of liquid water is 1 g/cm^3, so the initial volume of 1 liter can be converted to cubic centimeters:
Initial volume = 1 liter = 1000 cm^3
The density of ice is 0.917 g/cm^3, so the final volume of ice can be calculated as follows:
Final volume = mass / density = 1000 g / 0.917 g/cm^3 = 1090.16 cm^3
The change in volume is therefore:
ΔV = Final volume - Initial volume = 1090.16 cm^3 - 1000 cm^3 = 90.16 cm^3
Substituting the values into the equation for work:
Work = -PΔV = -(1 atm)(90.16 cm^3) = -90.16 atm cm^3
Since 1 atm cm^3 is equivalent to 101.325 joules, we can convert the units:
Work = -90.16 atm cm^3 × 101.325 joules / 1 atm cm^3 = -9,139.53 joules
Rounding to the nearest thousand, the amount of work exchanged is approximately -9,140 joules.
b) If this work could be converted into kinetic energy of this quantity of water, the speed would be approximately 34.5 m/s (78 mph)
The work done on the water during freezing can be converted into kinetic energy using the equation:
Work = ΔKE
Where ΔKE is the change in kinetic energy. The kinetic energy can be calculated using the equation:
KE = (1/2)mv^2
Where m is the mass of the water and v is the velocity (speed).
We know that the mass of the water is equal to its density multiplied by its volume:
Mass = density × volume = 1 g/cm^3 × 1000 cm^3 = 1000 g = 1 kg
Substituting the values into the equation for work:
-9,140 joules = ΔKE = (1/2)(1 kg)v^2
Solving for v:
v^2 = (-2)(-9,140 joules) / 1 kg = 18,280 joules/kg
v = √(18,280 joules/kg) ≈ 135.31 m/s
Converting the speed to mph:
Speed (mph) = 135.31 m/s × 2.237 ≈ 302.6 mph
Rounding to the nearest whole number, the speed is approximately 303 mph.
c) If the work of part (a) were used to raise this quantity of water by a distance h, the distance would be approximately 34.4 meters (113 feet).
The work done on the water during freezing can also be converted into potential energy using the equation:
Work = ΔPE
Where ΔPE is the change in potential energy. The potential energy can be calculated using the equation:
PE = mgh
Where m is the mass
of the water, g is the acceleration due to gravity, and h is the height.
We know that the mass of the water is 1 kg and the work done is -9,140 joules.
Substituting the values into the equation for work:
-9,140 joules = ΔPE = (1 kg)(9.8 m/s^2)h
Solving for h:
h = -9,140 joules / (1 kg)(9.8 m/s^2) ≈ -94 meters
The negative sign indicates that the water would be raised in the opposite direction of gravity. Since we are interested in the magnitude of the height, we take the absolute value.
Converting the height to feet:
Height (ft) = 94 meters × 3.281 ≈ 308.5 feet
Rounding to the nearest whole number, the height is approximately 309 feet.
Learn more about the calculations involved in determining the work, speed, and distance by considering the concepts of thermodynamics, phase changes, and energy conversions. Understanding these principles helps in comprehending how work is related to changes in volume, how kinetic energy can be derived from work, and how potential energy is associated with raising an object against gravity.
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Consider the vectors A=(-11.5, 7.6) and B=(9.6, -9.9), such that A - B + 5.3C=0. What is the x component of C?
Therefore, the x-component of C is approximately 3.98.
What is the relationship between velocity and acceleration in uniform circular motion?To solve the equation A - B + 5.3C = 0, we need to equate the x-components and y-components separately.
The x-component equation is:
A_x - B_x + 5.3C_x = 0Substituting the given values of A and B:
(-11.5) - (9.6) + 5.3C_x = 0Simplifying the equation:
-21.1 + 5.3C_x = 0To find the value of C_x, we can isolate it:
5.3C_x = 21.1Dividing both sides by 5.3:
C_x = 21.1 / 5.3Calculating the value:
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Starting from rest at the top of a frictionless inclined plane, a block takes 2 s to slide down to
the bottom.
The incline angle is 0, where sin 0 = 314 and cos 0 = 2/3.
What is the length of this inclined plane?
The length of an inclined plane can be determined based on the time that a block takes to slide down to the bottom of the plane, the angle of the incline, and the acceleration due to gravity. A block takes 2 s to slide down from the top of a frictionless inclined plane that has an angle of 0 degrees.
The sine of 0 degrees is 0.314 and the cosine of 0 degrees is 2/3.
To determine the length of the inclined plane, the following equation can be used:
L = t²gsinθ/2cosθ
where L is the length of the inclined plane, t is the time taken by the block to slide down the plane, g is the acceleration due to gravity, θ is the angle of the incline.
Substituting the given values into the equation:
L = (2 s)²(9.8 m/s²)(0.314)/2(2/3)
L = 38.77 m
Therefore, the length of the inclined plane is 38.77 meters.
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A sphere of radius R has uniform polarization
P and uniform magnetization M
(not necessarily in the same direction). Calculate the
electromagnetic moment of this configuration.
The electromagnetic moment of a sphere with uniform polarization P and uniform magnetization M can be calculated by considering the electric dipole moment due to polarization and the magnetic dipole moment due to magnetization.
To calculate the electromagnetic moment of the sphere, we need to consider the contributions from both polarization and magnetization. The electric dipole moment due to polarization can be calculated using the formula:
p = 4/3 * π * ε₀ * R³ * P,
where p is the electric dipole moment, ε₀ is the vacuum permittivity, R is the radius of the sphere, and P is the uniform polarization.
The magnetic dipole moment due to magnetization can be calculated using the formula:
m = 4/3 * π * R³ * M,
where m is the magnetic dipole moment and M is the uniform magnetization.
Since the electric and magnetic dipole moments are vectors, the total electromagnetic moment is given by the vector sum of these two moments:
μ = p + m.
Therefore, the electromagnetic moment of the sphere with uniform polarization P and uniform magnetization M is the vector sum of the electric dipole moment due to polarization and the magnetic dipole moment due to magnetization.
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a jogger jogs from one end to the other of a straight track in 2.50 min and then back to the starting point in 3.20 min. what is the jogger’s average speed
The distance of the run is 11.67 miles.
Speed is the unit rate in terms of distance travelled by an object and the time taken to travel the distance.
Speed is a scalar quantity as it only has magnitude and no direction.
Given that,
Speed of first jogger = 5 mph
Speed of second jogger = 4 mph
Let d be the distance in miles of the run.
Time taken by first jogger be t hours.
Time taken by second jogger = t + (35 minutes) = t + (7/12) hours
Speed = Distance / Time
5 = d / t and 4 = d / (t + 7/12)
d = 5t and d = 4 (t + 7/12)
5t = 4 (t + 7/12)
5t = 4t + 7/3
t = 7/3 hours
d = 5t = 11.67 miles.
Hence the distance ran by both joggers is 11.67 miles.
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A particle travels along a straight line with a constant acceleration. When s=4, v=14.23 and when s = 15,v= 20.59. Determine the velocity as a function of position
The velocity as a function of the position is v = 11.31 + (6.36 / 11) * t.
How to determine the velocity as a function of position?To estimate the velocity as a function of position, we shall use the equations of motion for uniformly accelerated motion.
Let:
s = the position of the particle
v = the velocity of the particle
a = the constant acceleration
Given:
When s = 4, v = 14.23
When s = 15, v = 20.59
We set up two equations using these values:
Equation 1: v² = u² + 2as
Equation 2: v = u + at
For the first set of values:
v₁ = 14.23
s₁ = 4
Applying Equation 2:
14.23 = u + 4a -----(3)
For the second set of values:
v₂ = 20.59
s₂ = 15
Using Equation 2:
20.59 = u + 15a -----(4)
Subtract Equation 3 from Equation 4:
20.59 - 14.23 = u + 15a - (u + 4a)
6.36 = 11a
a = 6.36 / 11
We substitute the value of a in Equation 3:
14.23 = u + 4 * (6.36 / 11)
14.23 = u + 2.92
Simplify:
u = 14.23 - 2.92
u = 11.31
So, the initial velocity (u) of the particle is 11.31 units.
Finally, we shall find the velocity (v) as a function of position (s) using Equation 2:
v = u + at
Putting the values of u and a:
v = 11.31 + (6.36 / 11) * t
Therefore, the velocity as a function of position (s) is:
v = 11.31 + (6.36 / 11) * t
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While attempting to tune the note C at 523Hz, a piano tuner hears 2.00 beats/s between a reference oscillator and the string.(b) When she tightens the string slightly, she hears 9.00 beats / s . What is the frequency of the string now?
The frequency of the string after it has been tightened slightly is 532 Hz. When the piano tuner hears 2.00 beats/s between the reference oscillator and the string, it means that the frequency of the string is slightly higher than the reference frequency.
To determine the frequency of the string after it has been tightened slightly, we can use the concept of beats in sound waves.
To calculate the frequency of the string, we can use the formula:
Frequency of string = Reference frequency + Beats/s
In this case, the reference frequency is given as 523 Hz (the note C), and the number of beats per second is 2.00. Plugging these values into the formula, we get:
Frequency of string = 523 Hz + 2.00 beats/s
Now, when the string is tightened slightly, the piano tuner hears 9.00 beats/s. We can use the same formula to find the new frequency of the string:
Frequency of string = Reference frequency + Beats/s
Again, the reference frequency is 523 Hz, and the number of beats per second is 9.00. Plugging these values into the formula, we get:
Frequency of string = 523 Hz + 9.00 beats/s
Simplifying the equation, we find that the new frequency of the string is 532 Hz.
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Consider two vectors: A = 12x + 19.5y B=4.4x -4.5y
What is the magnitude of the vector A-B? What is the angle of the vector A- B, measured counterclockwise in degrees from the positive x-axis?
The magnitude of the vector A-B is approximately 22.14 and the angle of the vector A-B is approximately 63.43 degrees.
What is the result of vector subtraction A - B, given the vectors A = 12x + 19.5y and B = 4.4x - 4.5y?The magnitude of the vector A-B can be calculated using the formula |A-B| = sqrt((Ax-Bx)² + (Ay-By)²), where Ax and Ay are the x and y components of vector A, and Bx and By are the x and y components of vector B.
The angle of the vector A-B can be calculated using the formula θ = atan2(Ay-By, Ax-Bx), where atan2 is the arctangent function that takes into account the signs of the components to determine the correct angle.
Please note that the specific values of the x and y components of vectors A and B are required to calculate the magnitude and angle.
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: 5. Five 50 kg girls are sitting in a boat at rest. They each simultaneously dive horizontally in the same direction at -2.5 m/s from the same side of the boat. The empty boat has a speed of 0.15 m/s afterwards. a. setup a conservation of momentum equation. b. Use the equation above to determine the mass of the boat. c. What
Five 50 kg girls are sitting in a boat at rest. They each simultaneously dive horizontally in the same direction at -2.5 m/s from the same side of the boat. The empty boat has a speed of 0.15 m/s afterwards.
a. A conservation of momentum equation is:
Final momentum = (mass of the boat + mass of the girls) * velocity of the boat
b. The mass of the boat is -250 kg.
c. Type of collision is inelastic.
a. To set up the conservation of momentum equation, we need to consider the initial momentum and the final momentum of the system.
The initial momentum is zero since the boat and the girls are at rest.
The final momentum can be calculated by considering the momentum of the girls and the boat together. Since the girls dive in the same direction with a velocity of -2.5 m/s and the empty boat moves at 0.15 m/s in the same direction, the final momentum can be expressed as:
Final momentum = (mass of the boat + mass of the girls) * velocity of the boat
b. Using the conservation of momentum equation, we can solve for the mass of the boat:
Initial momentum = Final momentum
0 = (mass of the boat + 5 * 50 kg) * 0.15 m/s
We know the mass of each girl is 50 kg, and there are five girls, so the total mass of the girls is 5 * 50 kg = 250 kg.
0 = (mass of the boat + 250 kg) * 0.15 m/s
Solving for the mass of the boat:
0.15 * mass of the boat + 0.15 * 250 kg = 0
0.15 * mass of the boat = -0.15 * 250 kg
mass of the boat = -0.15 * 250 kg / 0.15
mass of the boat = -250 kg
c. In a valid scenario, this collision could be considered an inelastic collision, where the boat and the girls stick together after the dive and move with a common final velocity. However, the negative mass suggests that further analysis or clarification is needed to determine the type of collision accurately.
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The complete question is:
Five 50 kg girls are sitting in a boat at rest. They each simultaneously dive horizontally in the same direction at -2.5 m/s from the same side of the boat. The empty boat has a speed of 0.15 m/s afterwards.
a. setup a conservation of momentum equation.
b. Use the equation above to determine the mass of the boat.
c. What type of collision is this?
a) The law of conservation of momentum states that the total momentum of a closed system remains constant if no external force acts on it.
The initial momentum is zero. Since the boat is at rest, its momentum is zero. The velocity of each swimmer can be added up by multiplying their mass by their velocity (since they are all moving in the same direction, the direction does not matter) (-2.5 m/s). When they jumped, the momentum of the system remained constant. Since momentum is a vector, the direction must be taken into account: 5*50*(-2.5) = -625 Ns. The final momentum is equal to the sum of the boat's mass (m) and the momentum of the swimmers. The final momentum is equal to (m+250)vf, where vf is the final velocity. The law of conservation of momentum is used to equate initial momentum to final momentum, giving 0 = (m+250)vf + (-625).
b) vf = 0.15 m/s is used to simplify the above equation, resulting in 0 = 0.15(m+250) - 625 or m= 500 kg.
c) The speed of the boat is determined by using the final momentum equation, m1v1 = m2v2, where m1 and v1 are the initial mass and velocity of the boat and m2 and v2 are the final mass and velocity of the boat. The momentum of the boat and swimmers is equal to zero, as stated in the conservation of momentum equation. 500*0 + 250*(-2.5) = 0.15(m+250), m = 343.45 kg, and the velocity of the boat is vf = -250/(500 + 343.45) = -0.297 m/s. The answer is rounded to the nearest hundredth.
In conclusion, the mass of the boat is 500 kg, and its speed is -0.297 m/s.
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both on you (a) What is the frequency of a light wave that has a wavelength of W nanometers? (h) A circular electric generator coil with Y loons has a radius of 0.05 meter and is
(a) The formula that relates the frequency, wavelength, and speed of light is c = λνwhere c is the speed of light, λ is the wavelength and ν is the frequency.
In order to determine the frequency of a light wave with a wavelength of W nanometers, we can use the formula ν = c/λ where c is the speed of light and λ is the wavelength. Once we convert the wavelength to meters, we can substitute the values into the equation and solve for frequency. The induced emf in a generator coil is given by the formula = N(d/dt), where N is the number of loops in the coil and is the magnetic flux.
To calculate the magnetic flux, we first need to calculate the magnetic field at the radius of the coil. This is done using the formula B = (0I/2r). Once we have the magnetic field, we can calculate the magnetic flux by multiplying the magnetic field by the area of the coil. Finally, we can substitute the values into the formula for induced emf and solve for the answer.
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An airplane's takeoff speed is 340 km/hkm/h .
If its average acceleration is 2.5 m/s2m/s2 , how much time is it accelerating down the runway before it lifts off?
Express your answer to two significant figures and include the appropriate units.
The time to accelerate is 37.76s. To calculate the time it takes for the airplane to accelerate down the runway before it lifts off, we can use the equation of motion:
v = u + at
Where:
v = final velocity (takeoff speed) = 340 km/h = 94.4 m/s
u = initial velocity (0 km/h as the airplane starts from rest) = 0 m/s
a = acceleration = 2.5 m/s²
t = time
To find the time, we rearrange the equation:
t = (v - u) / a
Substituting the given values, we have:
t = (94.4 m/s - 0 m/s) / 2.5 m/s²
t = 37.76 s
Therefore, the airplane accelerates down the runway for approximately 37.76 seconds before it lifts off.
The calculation is based on the equation of motion, which relates the final velocity of an object to its initial velocity, acceleration, and time. In this case, the final velocity is the takeoff speed of the airplane, the initial velocity is 0 (since the airplane starts from rest), the acceleration is given as 2.5 m/s², and we need to solve for the time.
By substituting the values into the equation and performing the calculation, we find that the time it takes for the airplane to accelerate down the runway before lifting off is approximately 37.76 seconds.
This means that the airplane needs this amount of time to reach its takeoff speed of 340 km/h with an average acceleration of 2.5 m/s².
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A hydroelectric power tacility converts the gravitational potential eneray of water benind a dam to electric enera. (tor each answer, enter a number.)
(a) What is the gravitational potential energv (in J) relative to the generators of a lake of volume 44.0 km~ (mass =
4.40 × 10^13- kg), given that the lake has an average height of 35.0 m above the
generators?
The answer is gravitational potential energy (in J) of the lake with respect to the generators is 1.52 x 10^17 J. The gravitational potential energy of the lake can be calculated using the formula: GPE = mgh where m is the mass of the water, g is the acceleration due to gravity, and h is the height of the lake relative to the generators. We can find the mass of the water using its volume and density. The density of water can be taken as [tex]1000 kg/m^3[/tex], so:
mass = volume x density = [tex](44.0 * 10^9 m^3) * (1000 kg/m^3) = 4.40 * 10^1^3 kg[/tex]
Substituting the values to calculate the GPE:
GPE = [tex](4.40 * 10^1^3 kg) * (9.81 m/s^2) * (35.0 m) = 1.52 * 10^1^7 J[/tex]
∴ The gravitational potential energy (in J) of the lake with respect to the generators is [tex]1.52 * 10^1^7 J[/tex].
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A high-performance dragster with a mass of
m = 1271 kg can accelerate at a rate of a = 25
m/s2.
If the track is L=400 m long, what is the numerical
value of the dragster’s final speed, vf in
m/s?
The dragster's final speed is approximately 141.42 m/s. To find the final speed of a high-performance dragster, we can use the given mass, acceleration, and track length.
By applying the kinematic equation relating distance, initial speed, final speed, and acceleration, we can calculate the numerical value of the dragster's final speed.
Using the kinematic equation, we have the formula: vf^2 = vi^2 + 2ad, where vf is the final speed, vi is the initial speed (which is assumed to be 0 since the dragster starts from rest), a is the acceleration, and d is the distance traveled.
Substituting the given values, we have vf^2 = 0 + 2 * 25 * 400.
Simplifying, we find vf^2 = 20000, and taking the square root of both sides, vf = sqrt(20000).
Finally, calculating the square root, we get the numerical value of the dragster's final speed as vf ≈ 141.42 m/s.
Therefore, the dragster's final speed is approximately 141.42 m/s.
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1. An oil drop is balanced in a Millikan apparatus. The drop has a mass of 1.8 10-18 kg. The plates have a potential difference of 920 V, are separated by 3.6 cm, and the lower plate is positive. Calculate the number of excess or deficit electrons on the oil drop, and state whether it is an excess or deficit. [5 marks)
The Millikan experiment was carried out to determine the value of the electric charge carried by an electron.'
The method was to suspend oil droplets in a uniform electric field between two metal plates by adjusting the voltage applied to the plates such that the force on the droplet was balanced by the force of gravity. The excess or deficit charge on the droplet could then be calculated and from this,
The charge carried by an electron could be determined.What is an oil drop?An oil drop is a charged droplet of oil that is formed in a high voltage field. An oil droplet carries an electric charge because when it comes into contact with an ion.
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