The direction of the force on the magnet and the direction of the magnetic field at the center of the loop due to the induced current both is to the right.
About Magnetic fieldBasically, the magnetic field is a vector field that describes the influence of a magnet on moving electric charges, electric currents, and other magnetic materials.
This method is formed by moving an electric current until it can create a force on a moving electric charge.
In short, it is the force field that exists around a conducting or magnetic object.
For example, the rotation of certain particles affected by an electric current can produce a magnetic field and a ferromagnetic (permanent) magnetic field.
This permanent magnetic field is also capable of attracting ferromagnetic materials, such as iron, and attracting or repelling other magnets.
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When an LED has 2 V applied to its terminals, it draws 100 mA and produces 2 mW of optical power. What is the LED's conversion efficiency from electrical to optical power?
The LED's conversion efficiency is the ratio of the optical power produced to the electrical power input. In this case, the LED has a conversion efficiency of 2 mW / (2 V * 100 mA) = 0.02, or 2%.
This means that 2% of the electrical power applied to the LED is converted into optical power, while the rest is lost as heat. This conversion efficiency is a measure of how effectively the LED converts electrical energy into light. To improve the LED's efficiency, engineers may work to reduce the amount of electrical energy lost as heat, or to increase the amount of electrical energy that is converted into light.
The LED's conversion efficiency is the ratio of the optical power produced to the electrical power input. In this case, the LED has a conversion efficiency of 2 mW / (2 V * 100 mA) = 0.02, or 2%.
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Ima Rilla Saari rushes to her car in order to hurry home and get dressed for work. Failing to realize the dangers of driving under slick and icy conditions, she collides her 964.0-kg Mazda Miata into the rear of a 3280.0-kg pick-up truck which was at rest at the light on Lake Avenue. Ima's pre-collision speed was 12.1 m/s. Determine the 3280.0-collision speed of the two entangled cars as they slide across the ice.
Answer:
The collision speed of the two cars is 8.8 m/s.
What is the relation between wavelength and period of a wave?
The primary distinction between wavelength and period is that the former measures the shortest path between consecutive locations on a wave that are in phase, while the latter measures the amount of time needed for an oscillation to complete at a particular position.
What is the formula for a wave's period?T = 1 / f, where "T" stands for the period, or the length of time it takes for one cycle to complete, and "f" stands for frequency, which is the formula for the period. Convert frequency from Hertz to 1/s to obtain period from frequency. Multiply 1 by the frequency now. Time (period) given in seconds will be the outcome.
What are SI units and wavelengths?A meter, commonly abbreviated as m, is the SI unit of wavelength. The multiples or fractions of a meter are also used to measure wavelength. Notably, when wavelengths are a significant feature, exponential powers of 10 are used. Shorter wavelengths are described as having a negative exponential.
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Two
Imagine an alternate universe where the value of the Planck constant is 6.62607 x 108 J.S.
In that universe, which of the following objects would require quantum mechanics to describe, that is, wou
objects would act like everyday objects, and be adequately described by classical mechanics?
object
A grain of sand with a mass of 170 mg, 670. um wide,
moving at 4.00 mm/s.
An eyelash mite with a mass of 13.5 µg, 270 um wide,
moving at 31. um/s..
An airplane with a mass of 1.88 x 10 kg, 14.0 m long,
moving at 1500. km/h.
A turtle with a mass of 480. g, 28. cm long, moving at 1.6
cm/s.
quantum or classical?
A grain of sand with a mass of 170 mg, 670. um wide, moving at 4.00 mm/s - Classical.
What is mass?Mass is the measure of an object’s inertia, or its resistance to changes in motion. It is a fundamental property of matter and is typically measured in kilograms. It is different from weight, which is a measure of the force of gravity acting on an object.
An eyelash mite with a mass of 13.5 µg, 270 um wide, moving at 31. um/s. - Quantum
An airplane with a mass of 1.88 x 10 kg, 14.0 m long, moving at 1500. km/h - Classical
A turtle with a mass of 480. g, 28. cm long, moving at 1.6 cm/s. - Classical
All of the objects in question are macroscopic, meaning that their behavior can be accurately described with classical mechanics. However, because the Planck constant is larger than its value in our universe, the eyelash mite is at the limit of being small enough to require quantum mechanics to describe its behavior. Therefore, it would be the only object that would require quantum mechanics in this alternate universe.
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a 10-cm -long thin glass rod uniformly charged to 13.0 nc and a 10-cm -long thin plastic rod uniformly charged to -13.0 nc are placed side by side, 4.50 cm apart. what are the electric field strengths e1 to e3 at distances 1.0 cm , 2.0 cm , and 3.0 cm , from the glass rod along the line connecting the midpoints of the two rods?
A. At a point 1cm from the glass rod, E = 1.36 × 10⁶ N/C
B. At a point 2cm from the glass rod, E = 5.17 × 10⁵ N/C
C. At a point 3cm from the glass rod, E = 6.993 × 10⁵ N/C
How to calculate electric filed strength?Parameters given:
Charge of glass rod, Q = 14nC = 14 × 10⁻⁹ C
Charge of plastic rod, q = 14nC = 14 × 10⁻⁹ C
Distance between both rods = 4.5cm = 0.045
A. Electric field strength at a point 1.0cm (0.01m) from the glass rod is the sum of electric field strength due to both rods i.e.
E = E₁ + E₂
Where
E₁ = electric field strength due to glass rod
E₂ = electric field strength due to plastic rod
E₁ = kQ/0.01²
E₂ = kq/(0.045 - 0.01)² = kq/(0.035)²
E = kQ/0.01² + kq/(0.035)² = k(Q/0001 + q/0.001225)
E = 9 * 10⁹ [(14 * 10⁻⁹ / 0.001) + (14 * 10⁻⁹)/0.001225]
E = 9 * 10⁹[(14 * 10⁻⁵) + (1.143 * 10⁻⁵)]
E = 9 * 10⁹ * 15.143* 10⁻⁵
E = 1.36 × 10⁶N/C
B. Electric field strength at a point 2.0cm (0.02m) from the glass rod is the sum of electric field strength due to both rods i.e.
E = E₁ + E₂
E₁ = kQ/0.02²
E₂ = kq/(0.045 - 0.02)² = kq/(0.025)²
E = kQ/0.02² + kq/(0.025)² = k(Q/0.0004 + q/0.000625)
E = 9 * 10⁹ [(14 * 10⁻⁹ / 0.0004) + (14 * 10⁻⁹)/0.000625]
E = 9 * 10⁹[(3.5 * 10⁻⁵) + (2.24 * 10⁻⁵)]
E = 9 * 10⁹ * 5.74 * 10⁻⁵
E = 5.17 × 10⁵ N/C
C. Electric field strength at a point 3.0cm (0.03m) from the glass rod is the sum of electric field strength due to both rods i.e.
E = E₁ + E₂
E₁ = kQ/0.03²
E₂ = kq/(0.045 - 0.03)² = kq/(0.015)²
E = kQ/0.03² + kq/(0.015)² = k(Q/0009 + q/0.000225)
E = 9 * 10⁹ [(14 * 10⁻⁹ / 0.009) + (14 * 10⁻⁹)/0.000225]
E = 9 * 10⁹[( 1.55 * 10⁻⁵) + (6.22 * 10⁻⁵)]
E = 9 * 10⁹ * 7.77 * 10⁻⁵
E = 6.993 × 10⁵ N/C
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according to newton's law of inertia, a railroad train in motion should continue going forever even if its engine is turned off. we never observe this because railroad trains are much too heavy. move too slowly. always have forces that oppose the motion. must go up and down hills.
According to Newton's law of inertia, a railroad train in motion should continue going forever even if its engine is turned off.
We never observe this because railroad trains are much too heavy and therefore require a great deal of energy to keep them moving.
Additionally, railroad trains move too slowly for the effects of inertia to be easily visible, and they are also subject to opposing forces such as air resistance, friction and gravity which slow them down and eventually bring them to a stop. Finally, railroad trains must go up and down hills, and this requires additional energy which is not available after the engine is turned off.
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If you were standing on the South Pole (with the south celestial pole in your zenith) atthe time of the vernal equinox, where would you see the Sun all day? A)On your horizon C)23.5° above the horizon B)Well below your horizon D)In your zenith
If you were standing at the South Pole during the vernal equinox (around March 20th-21st), the Sun would be well below your horizon all day.
At the time of the vernal equinox, the Sun is directly overhead at the equator. At the South Pole, the equator is to the north and the Sun is always below the horizon. If you were standing on the South Pole at the time of the vernal equinox, you would see the Sun well below the horizon. The vernal equinox marks the time when the Sun's rays are directly overhead at the equator. At the South Pole, however, the Sun is always located to the north of the observer, so it is always below the horizon and never rises or sets. As a result, the Sun remains well below the horizon at the South Pole throughout the day, even at the time of the vernal equinox.
Therefore, the answer is B) Well below your horizon.
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letter “c” is pointing to the force variable in the graph . What letter in physics is used to represent force
Answer:
Explanation:
Newton
Calculate the wavelength of Radio 4 which broadcasts on a frequency of 198 kHz?
Answer:
The wavelength of Radio 4, which broadcasts on a frequency of 198 kHz, is approximately 15.152 meters.
Explanation:
The wavelength of a radio wave is calculated by dividing the speed of light (approximately 3 x 10^8 meters per second) by the frequency of the wave.
To calculate the wavelength of Radio 4, which broadcasts on a frequency of 198 kHz, we can use the following equation:
wavelength = (speed of light) / (frequency)
wavelength = (3 x 10^8 m/s) / (198 x 10^3 Hz)
wavelength = 15.152 meters
So the wavelength of Radio 4, which broadcasts on a frequency of 198 kHz, is approximately 15.152 meters.
what effect or effects would be most significant if the moon's orbital plane were exactly the same as the ecliptic plane? group of answer choices solar eclipses would be much more frequent. solar eclipses would last much longer. solar eclipses would be much rarer.
Solar eclipses would be much more frequent if the moon's orbital plane were the same as the ecliptic plane
What is ecliptic plane?
The ecliptic plane is defined as the imaginary plane containing the Earth's orbit around the sun. In the course of a year, the sun's apparent path through the sky lies in this plane.The ecliptic is so named because the ancients noted that eclipses only occur when the Moon is crossing it.Ecliptic, in astronomy, the great circle that is the apparent path of the Sun among the constellations in the course of a year; from another viewpoint, the projection on the celestial sphere of the orbit of Earth around the Sun. The constellations of the zodiac are arranged along the ecliptic.The Earth orbits the Sun on a particular angle and its orbit is elliptical in shape. The orbit is often shown as an ellipse made of dotted lines with the Sun at its center. If you made this ellipse a solid surface and extended it infinitively, then you would have the plane of the ecliptic.To learn more about ecliptic plane refers to:
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the following three hot samples have the same temperature. the same amount of heat is removed from each sample. which one experiences the smallest drop in temperature,and which one experiences the largest drop? sample a. 4.0 kg of water sample b. 2.0 kg of oil sample c. 4.0 kg of dirt
Sample A of 4.0 kg of water would experience the smallest drop in temperature since water has a higher specific heat capacity than oil and dirt.
This means that water requires much more energy to heat or cool by the same amount as oil or dirt. Therefore, when the same amount of heat is removed from each sample, the water sample experiences the smallest drop in temperature.
Sample C of 4.0 kg of dirt would experience the largest drop in temperature due to its low specific heat capacity, meaning that it takes less energy to heat or cool dirt than water or oil.
Therefore, when the same amount of heat is removed from each sample, the dirt sample would experience the largest drop in temperature.
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use the scalar triple product to determine if the vectors u = i 4j − 2k, v = 2i − j, and w = 5i 11j − 6k are coplanar.
Answer:
40
Explanation:
as they are coplanar det =0
so =1(6)-4(-12)+(-2)(22-5)
=6+48-14
=40
Yes, they are coplanar as the scalar triple product is 0.
What is scalar triple product?
It is clear from the name alone that the scalar triple product of vectors refers to the combination of three vectors. It entails combining the cross product of the final two vectors with the dot product of one of the vectors. It's represented as [a b c] = (a b) c
Looking at the formula above, the following conclusions can be made:
i) A scalar quantity is always the resultant.
ii) The scalar triple product is calculated by first calculating the cross product of the vectors, then the dot product.
iii) The volume of the parallelepiped, whose three coterminous edges reflect the three vectors a, b, and c, is what the scalar triple product formula physically represents.
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What is the gage pressure at the bottom of the tank filled with water to a depth of 5 ft when the tank accelerates upward at a rate of 3.0 ft/s2. p= __ psi
80.0 psi is the gage pressure at the bottom of the tank filled with water to a depth of 5 ft when the tank accelerates upward at a rate of 3.0 ft/s2.
To determine the gage pressure at the bottom of the tank, we need to calculate the pressure difference due to the acceleration of the tank and the pressure due to the weight of the water. The pressure due to the weight of the water can be calculated using the equation
=> p = ρgh,
here,
p is pressure,
ρ is density of water,
g is acceleration due to gravity,
and h is height of the water column.
The density of water = 62.4 lb/ft^3
Acceleration (gravity) is 32.2 ft/s^2.
Hence,
=> p = ρgh
= 62.4 lb/ft^3 x 32.2 ft/s^2 x 5 ft
= 10080 lb/ft^2
Next, we need to calculate the pressure difference due to the acceleration of the tank. The pressure difference due to acceleration can be calculated using the equation:-
=> Δp
= ρV^2/2g,
here,
V is velocity of the fluid,
g is acceleration due to gravity.
We can assume that the velocity of the fluid at the bottom of the tank is zero, and the acceleration of the tank is 3.0 ft/s^2.
Hence,
=> Δp = ρV^2/2g
= 62.4 lb/ft^3 x (3.0 ft/s^2)^2 / 2 x 32.2 ft/s^2
= 623.04 lb/ft^2
Finally, the gage pressure at the bottom of the tank can be calculated by adding the pressure due to the weight of the water and the pressure difference due to the acceleration of the tank. The gage pressure is given in pounds per square inch (psi), which can be converted from pounds per square foot by dividing by 144.
Hence,
=> p = (p + Δp) / 144
= (10080 + 623.04) lb/ft^2 / 144
= 80.0 psi
Therefore, the gage pressure at the bottom of the tank filled with water to a depth of 5 ft when the tank accelerates upward at a rate of 3.0 ft/s^2 is 80.0 psi.
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how much energy must be used to produce 4.75 mol of gaseous water?: h20 (l) 44.0 kj -→ h2o (g) select one: a. 207kj b. 9.362 kj c. 206.8 kj d. 9.36kj
The amount of energy must be used to produce 4.75 mol of gaseous water is : 206.8 kJ. The correct alternative is option C.
To calculate the amount of energy required to produce 4.75 moles of gaseous water, we use the enthalpy of vaporization formula.
The enthalpy of vaporization of water is the amount of energy required to turn a given amount of liquid water into gaseous water at a constant temperature.
The enthalpy of vaporization of water is 44.0 kJ/mol.So, to convert 4.75 moles of liquid water into gaseous water, we multiply the enthalpy of vaporization by the number of moles:44.0 kJ/mol * 4.75 moles = 206.8 kJ.
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what is the linear charge density of a thin wire bent into a circle (or ring) of radius 7.48 cm if the total charge on the wire is 3.76 µc?
The required value of linear charge density of a thin wire bent into a circle is 0.08 × 10⁻⁴ c/m.
The wire is curved into a circular form.
The radius of the circle is given as R = 7.48 cm = 7.48 × 10⁻² m
The total charge on the wire Q = 3.76 µc = 3.76 × 10⁻⁶ c
The relation between total charge, radius and linear charge density is known as,
Q = 2 π R α
where, Q is the total charge
R is the radius of the wire bent into a circle
α is linear charge density
Making α as subject, we have,
α = Q /(2 π R) = (3.76 × 10⁻⁶)/(2 π ×7.48 × 10⁻²) = (3.76 × 10⁻⁶)/(46.97 × 10⁻²) = 0.08 × 10⁻⁴ c/m
Thus, the value of linear charge density of a thin wire is calculated to be 0.08 × 10⁻⁴ c/m.
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determine the ultimate load of a rectangular footing with dimensions of 6x4 wiht eccentric load
Without additional information, the ultimate load of a rectangular foundation with 6 x 4 dimensions that is being subjected to an eccentric load cannot be computed.
The ultimate load capacity of the footing is influenced by a number of variables, including the material properties, the soil characteristics, and the size and placement of the eccentric load.
It would be necessary to conduct a structural study taking into account the footing's geometry, material qualities, and load circumstances in order to calculate the ultimate load. For the analysis to establish the maximum load that the footing can support, calculations for soil bearing capacity, shear strength, and bending moments are commonly used. It is significant to highlight that a competent engineer who is knowledgeable should carry out the computations.
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If the tank to hold this water is 1.500 meters tall, what is the average velocity of a liter of water when it flows out of a faucet 1.000 meters above the floor on the ground floor?
The average velocity of a liter of water when it flows out of a faucet 1.000 meters above the floor on the ground floor is 1.82 m/s.
What is the time of motion of the water?The time taken for the water to fall from the given height is calculated as follows;
t = √ ( 2h / g )
where;
h is the height of fall of the waterg is acceleration due to gravityt = √[ ( 2 x 1.5 ) / ( 9.8 ) ]
t = 0.55 second
The average velocity of a liter of water when it flows out of a faucet 1.000 meters above the floor on the ground floor;
v = d / t
v = ( 1 m ) / ( 0.55 s )
v = 1.82 m/s
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what is the mechanical advantage of a first class lever that has an input force of 200 N and produces and output force of 1300 N
A bra rod i 2m long at a certain temperature. What i it length for temperature rie of 100k,if the expanivity of bra i 18×10-6k-1
The length of brass rod after expansion is 2.0036m.
How to calculate length?By definition, the length increase is:
Delta L = Alpha L_0 Delta TΔL=αL
naΔT
where alpha = 18 times 10^{-6}K^{-1}α=18×10−6
K-1
is expansion, L0 = 2 ml
na=2m is the initial length and Delta T = 100KΔT=100K is the temperature change. How to get:
Delta L = 18 times 10^{-6}cdot 2cdot 100 = 3.6 times 10^{-3} = 0.0036mΔL=18×10
−6
⋅2⋅100=3.6×10
−3
= 0.0036 meters
So the final length is:
L = L0 + delta L = 2 m + 0.0036 m = 2.0036 ml = l
0
na
+ΔL=2m+0.0036m=2.0036m
Linear expansion is the rate of increase in length of a solid sample per unit rise in temperature. If the length of the sample increases from l1 to l2 as the temperature increases by θ°, the expansion (α) is given by
l2 = l1(1 + αθ). This relationship assumes that α is independent of temperature.
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hat is a property of electric potential energy? always a negative value inversely proportional to the distance between subject and source a vector quantity with direction determined by the electric flux independent of the subject's charge
The electric potential energy is inversely proportional to the distance between subject and source. Option a is the correct answer.
The electric potential energy of any given charge or system of charges is termed as the total work done by an external agent in bringing the charge or the system of charges from infinity to the present configuration without undergoing any acceleration.
Electrostatic potential energy is given by the formula, U = [1/(4πεo)] × [q1q2/d].
where, q1, q2 are the electric charges,
d is the distance between the charges.
As per the formula, the energy is inversely proportional to the distance between subject and source.
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--The complete question is, Which of these below is a property of electric potential energy of point charges?
a) inversely proportional to the distance between subject and source
b) independent of the subject's charge
c) a vector quantity with direction determined by the electric flux
d) always a negative value--
what fraction of the incident intensity of a sound pulse will be reflected when sound travels from fat into lung? express your answer in percent.
The fraction of incident intensity of a sound pulse that will be reflected when sound travels from fat into lung is 58.24%
What is sound?An elastic material medium allows sound, a mechanical disturbance from an equilibrium state, to travel through it. It is also possible to define sound solely subjectively, as that which is perceived by the ear. However, this definition lacks clarity and is overly constrictive, as it is useful to discuss sounds that are produced by devices other than the human ear, such as dog whistles and sonar equipment, which cannot be heard by the human ear.
Starting with the characteristics of sound waves is important when studying sound. Transverse and longitudinal waves are the two basic types of waves, which are distinguished by the way in which the wave moves.
[tex]$$\rho=$ Density of material\\$\mathrm{c}=$ Acoustic velocity\\\\Impedance is given by$$Z=\rho c$$Acoustic impedance of lung$$Z_l=\rho_l c_l=0.18 \times 10^6 \mathrm{kgs} / \mathrm{m}^2$$Acoustic impedance of fat$$Z_f=\rho_f c_f=1.34 \times 10^6 \mathrm{kgs} / \mathrm{m}^2$$[/tex]
[tex]$$Reflection coefficient is given by$$\begin{aligned}& R=\left(\frac{Z_l-Z_f}{Z_l+Z_f}\right)^2 \\& \Rightarrow R=\left(\frac{0.18 \times 10^6-1.34 \times 10^6}{0.18 \times 10^6+1.34 \times 10^6}\right)^2 \\& \Rightarrow R=0.5824\end{aligned}$$[/tex]
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Complete question:
consider the differential equation with initial condition . a. use euler's method with two steps to estimate when : 2 (be sure not to round your calculations at each step!) now use four steps: 3.25 (be sure not to round your calculations at each step!) b. what is the solution to this differential equation (with the given initial condition)? 4.5 c. what is the magnitude of the error in the two euler approximations you found? magnitude of error in euler with 2 steps
To find an approximate solution to the given differential equation with the given initial condition, you can use Euler's method with two steps.
The approximate solution at t = 2 is 3.25 and with four steps is 4.5. The magnitude of the error in the two Euler approximations you found would be the difference between the two approximate solutions, which is 1.25.
To further explore Euler's method, it is important to understand the concept of numerical errors. In the numerical solution of a differential equation, numerical errors occur when the approximate solution is not close enough to the true solution. These errors can be caused by a variety of factors, including the choice of numerical method, the step size used in the method, the number of steps taken, and the accuracy of the initial conditions.
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a car moving with a constant velocity travels 100 meters in 2 seconds. what was the average velocity of the car in m/
The average velocity of the car in m/s is: 50 m/s
What is velocity?It is a physical quantity that indicates the displacement of a mobile per unit of time, it is expressed in units of distance per time, for example (miles/h, km/h).
The formula and procedure we will use to solve this problem is:
v= x/t
Where:
x = distancet = timev = velocityInformation about the problem:
x = 100 mt = 2 sv=?Applying the velocity formula we get:
v = 100 m / 2 s
v = 50 m/s
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suppose that fred’s velocity is vf (t) = 20t cos(πt) meters/minute and marie’s velocity is vm(t) = 30t sin(πt) meters/minute at time t minutes after the start of a race.
The time at which Fred and Marie have the same velocity is t = 0.
Determine the velocity difference between Fred and Marie.
Difference in velocity = vf(t) - vm(t)
= 20t cos(πt) - 30t sin(πt)
= 10t[cos(πt) - sin(πt)] meters/minute
The velocity difference's magnitude should be determined.
Magnitude of the difference in velocity = |10t[cos(πt) - sin(πt)]|
= |10t| |cos(πt) - sin(πt)|
Determine the moment when Fred and Marie move at the same speed.
Make the velocity difference equal to 0.
0 = 10t[cos(πt) - sin(πt)]
To convert the equation into terms of t 0 = 10t2, multiply both sides by t.
0 = 10t²[cos(πt) - sin(πt)]
To get an equation in terms of cos(πt) and sin(πt), divide both sides by 10t².
0 = [cos(πt) - sin(πt)]
Solve for t by setting cos(πt) = sin(πt)
cos(πt) = sin(πt)
πt = arcsin(sin(πt))
πt = arcsin(cos(πt))
πt = arccos(cos(πt))
Fred and Marie's velocities are equal at time t = 0, or at that instant.
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if you have a cart rolling down an inclined track and wish to calculate the acceleration of the cart, what value do you need to know about the track-cart system?
Acceleration on a ramp equals the ratio of the height to the length of the ramp, multiplied by gravitational acceleration.
What is track-cart system?
The Dynamics Cart and Track System provides students with the tools they need to explore kinematics, dynamics, momentum, and energy. This versatile system can also be easily adapted to study optics, color, and diffraction.A set of dynamic cart trolleys are used for investigation on momentum, velocity and acceleration. Each trolley consists of two rectangular wooden blocks, 300 mm long, moving on three low friction wheels (ball bearings in wheels). The trolley is fitted with spring loaded impulse rod.The Dynamics Cart and Track System provides students with the tools they need to explore kinematics, dynamics, momentum, and energy.Each cart is 310 x 310 x 90mm. Mass per cart is 600 grams. Cart colour is grey.To learn more about track-cart refers to:
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an object moves according to the function x = t7/2 where x is the distance traveled and t is the time. its kinetic energy is proportional to:
The kinetic energy of the object which moves according to the function x = t7/2 is proportional to t^5.
The kinetic energy (KE) of an object is proportional to its mass (m) and the square of its velocity (v). If x = t^(7/2) is the equation for the distance traveled by the object, then its velocity (v) can be obtained by taking the derivative of x with respect to time (t).
v = dx/dt = (7/2)t^(5/2)
So the kinetic energy can be calculated as:
KE = 1/2 * m * v^2 = 1/2 * m * [(7/2)t^(5/2)]^2 = (49/8) * m * t^5
Therefore, the kinetic energy of the object is proportional to t^5.
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a red blood cell contains 2.7 107 free electrons. what is the total charge of these electrons in the red blood cell?
The total charge of these electrons in the red blood cell - 4.3 × 10⁻¹² Coulombs. The result is obtained by multiplying the number of electrons by the charge or each electrons.
What is charge?Charge is a physical property of subatomic particles that causes objects experience a attractive force toward one another.
An electron has the charge of - 1.602 × 10⁻¹⁹ Coulombs. If there are n electron, the charge is
q = ne
Where
q = chargen = number of electrone = charge of an electronA red blood cell contains 2.7 × 10⁷ electrons.
Find the total charge!
The total charge of the electrons in the red blood cell is
q = ne
q = 2.7 × 10⁷ × (- 1.602 × 10⁻¹⁹)
q = - 4.3 × 10⁻¹² Coulombs
Hence, in the red blood cell, the total charge of the electrons is - 4.3 × 10⁻¹² Coulombs.
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which moment corresponds to the maximum kinetic energy of the system? view available hint(s)for part d which moment corresponds to the maximum kinetic energy of the system? a b c d consider the block in the process of oscillating. if the kinetic energy of the block is increasing, the block must be consider the block in the process of oscillating.if the kinetic energy of the block is increasing, the block must be at the equilibrium position. at the amplitude displacement. moving to the right. moving to the left. moving away from equilibrium. moving toward equilibrium. to learn to apply the law of conservation of energy to the analysis of harmonic oscillators. systems in simple harmonic motion, or harmonic oscillators, obey the law of conservation of energy just like all other systems do. using energy considerations, one can analyze many aspects of motion of the oscillator. such an analysis can be simplified if one assumes that mechanical energy is not dissipated. in other words, e
The answers for Part A = A, Part B = A, Part C = moving toward equilibrium, Part D = C, Part E = C, Part F = D, and Part G = 3/8kA².
For part A: The maximum PE is when the spring is fully compressed. D might look like the correct answer, but actually, A is when the spring is at amplitude. Even though it’s stretched, that still counts as compression: A
For part B: When PE is maximized, KE is minimized, so the correct answer is the same as from Part A: A
For part C: KE is maximized when PE is minimized. PE is most prominent at amplitude, and KE is most prominent at equilibrium. So choice F is correct: F. moving toward equilibrium.
For part D: KE is greatest at equilibrium: C
For part E: Minimum PE is when KE is greatest, i.e. at equilibrium: C
For part F: When U = KE, U = 1/2Umax (this is just a fact, which we won’t bother solving for here). So:
U = 1/2(U)
1/2kx² = 1/2(1/2kA²)
x² = 1/2A²
x = √(1/2A²)
x = A√(2)/2
Note- if it isn’t obvious where the √(2)/2 came from, use 2/4 for the fraction above instead of 1/2:
x = √((2/4)A²)
x = A√(2)/2
The diagram doesn’t give this as an answer, but it does give -A√(2)/2, which is equivalent: D
For part G: Since total energy = KE + PE and we only have enough information to find PE, we can work backwards by first finding the maximum PE and then subtracting the PE at point B.
Maximum PE:
PE(max) = 1/2kA²
PE at Point B:
PE(B) = 1/2k(A/2)²
PE(B) = 1/2k(A²/4)
PE(B) = 1/8k(A²)
Now find the difference between the Potential energies, and that difference must be kinetic energy since there is no friction:
KE(B) = PE(max) – PE(B)
KE(B) = 1/2kA² – 1/8k(A²)
KE(B) = 3/8kA²
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--The given question is incomplete; the complete question is
" Consider a harmonic oscillator at four different moments, labelled A, B, C, and D, as shown in the figure. Assume that the force constant k, the mass of the block, m, and the amplitude of vibrations, A, are given. Answer the following questions:
Part A
Which moment corresponds to the maximum potential energy of the system?
A
B
C
D
Part B
Which moment corresponds to the minimum kinetic energy of the system?
A
B
C
D
Part C
Consider the block in the process of oscillating. If the kinetic energy of the block is increasing, the block must be:
A. at the equilibrium position.
B. at the amplitude displacement.
C. moving to the right.
D. moving to the left.
E. moving away from equilibrium.
F. moving toward equilibrium.
Part D
Which moment corresponds to the maximum kinetic energy of the system?
A
B
C
D
Part E
Which moment corresponds to the minimum potential energy of the system?
A
B
C
D
Part F
At which moment is K = U?
A
B
C
D
Part G
Find the kinetic energy K of the block at the moment labelled B.
Express your answer in terms of k and A."--
A profeional ladder climber with a ma of 77 kg climb a 6 m tall ladder in 1. 3 econd. How much horepower did the ladder climber produce? (round to 1 decimal place if needed)
The ladder climber produced 4.7 Horsepower to climb a ladder of 6 meter height in 1.3 seconds.
Mass of the ladder climber, m = 77 kg
Height of the ladder, h = 6 m
Time, t = 1.3 sec
Energy to climb the ladder will be equal to the potential energy of the ladder climber at 6 m height. So the potential energy will be, p = mgh
p = 77 × 9.81 × 6
p = 4532.22 Joules
Power is defined as the time rate of doing a work. So, power = work/time
Power = 4532.2/1.3 = 3486.32 J/S
Power in horsepower = 3486.32/746 = 4.7 Horsepower
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the displacement in meters of a certain vibrating mass is described by x(t)=0.005sin6t. what is the amplitude and frequency of its velocity
The object oscillates about the equilibrium position x0. such that x0 = 0, then the displacement x from the equilibrium position as a function of time is given by x(t) = A cos(ωt + φ).
A is the amplitude of the oscillation, i.e. the maximum displacement of the object from equilibrium, either in the positive or negative x-direction. Simple harmonic motion is repetitive. The period T is the time it takes the object to complete one oscillation and return to the starting position. The angular frequency ω is given by ω = 2π/T. The angular frequency is measured in radians per second. The inverse of the period is the frequency f = 1/T. The frequency f = 1/T = ω/2π of the motion gives the number of complete oscillations per unit time. It is measured in units of Hertz, (1 Hz = 1/s).
The velocity of the object as a function of time is given by
v(t) = -ω A sin(ωt + φ),
and the acceleration is given by
a(t) = -ω2A cos(ωt + φ) = -ω2x.
The quantity φ is called the phase constant. It is determined by the initial conditions of the motion. If at t = 0 the object has its maximum displacement in the positive x-direction, then φ = 0, if it has its maximum displacement in the negative x-direction, then φ = π. If at t = 0 the particle is moving through its equilibrium position with maximum velocity in the negative x-direction then φ = π/2. The quantity ωt + φ is called the phase.
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