Given Data:
Helium is pumped into a spherical balloon at a rate of 5 cubic feet per second.
Volume of a sphere is given by V= (4/3) π r³
To Find: Rate of change of radius (in feet per second)
Formula used: V= (4/3) π r³Differentiating V w.r.t t, we get d V/dt = 4πr² . dr/dt
Solution: Given that helium is pumped into a spherical balloon at a rate of 5 cubic feet per second and it is required to find the rate of change of radius (in feet per second) after 3 minutes.
Let’s first convert the given time into seconds;
3 minutes = 3 × 60 seconds = 180 seconds.
Volume of the spherical balloon (V) pumped with helium = Rate of helium pumped into the balloon = 5 cubic feet per second
As per the formula of the volume of a sphere,V = (4/3) π r³ ⇒ r³ = (3/4π) V Differentiating with respect to time t, we get,3r² . d r/d t = (3/4π) d V/d t Multiplying both sides by (4/3π), we get, dr/dt = (4/3π) (d V/d t) / 3r²
Given that d V/d t = 5, we get, d r/d t = (4/3π) (5) / 3r²
We are given that we need to find the value of the rate of change of the radius after 3 minutes i.e t = 180 seconds. Putting the value of t in the above equation, we get, /d t = (4/3π) (5) / 3r²dr/d t = (20/9πr²) feet/second
Now, we need to find the value of r;
as per the formula of volume, V = (4/3) π r³V = (4/3) π (2)³ ⇒ 33.51 cubic feet Therefore, r = (3V/4π)^(1/3) = (3×33.51/4π)^(1/3) = 2 feet (approx.) Putting the value of r in the above equation,
we get, d r/d t = (20/9π(2)²) feet/second d r/d t = (5/18π) feet/second
Therefore, the rate of change of the radius of the balloon after 3 minutes is (5/18π) feet/second.
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what is the internal resistance (in ω) of an automobile battery that has an emf of 12.0 v and a terminal voltage of 14.5 v while a current of 8.30 a is charging it? ω
The internal resistance of the automobile battery is 0.3012 Ω.
The internal resistance of an automobile battery that has an emf of 12.0 V and a terminal voltage of 14.5 V while a current of 8.30 A is charging can be calculated using the formula,
`V = E - Ir` where `V` is the terminal voltage, `E` is the emf, `I` is the current and `r` is the internal resistance.
So, we can write the formula as
`r = (E - V)/I`.
Substituting the given values, we get,
r = (12.0 - 14.5)/8.30r = -2.5/8.30r = -0.3012 Ω.
Since resistance cannot be negative, we can take the magnitude of it. Hence, the internal resistance of the automobile battery is 0.3012 Ω. In physics, resistance is the ability of a material to oppose the flow of electrical current. It is represented by the symbol R and is measured in ohms (Ω). Resistance is dependent on various factors such as the material of the conductor, its length, its cross-sectional area, and temperature. When a voltage is applied across a conductor, an electrical current flows through it. However, some of the electrical energy is dissipated in overcoming the resistance of the conductor, which generates heat. Therefore, resistance leads to the loss of electrical energy.
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if you throw a ball against the ceiling—so the ball moves upward and then rebounds to move downward—at the instant the ball hits the ceiling, the acceleration is
a.Zero.
b. Positive.
d. Negative.
If you throw a ball against the ceiling—so the ball moves upward and then rebounds to move downward, at the instant the ball hits the ceiling, the acceleration is d. Negative.
When the ball hits the ceiling, it experiences a sudden change in its motion. Before hitting the ceiling, the ball is moving upward with a positive velocity and experiencing a positive acceleration due to the force of gravity pulling it down. However, upon hitting the ceiling, the direction of motion changes, and the ball starts moving downward. As a result, its velocity becomes negative, and the acceleration also becomes negative to oppose the motion and slow down the ball's upward velocity. Therefore, the acceleration at the instant the ball hits the ceiling is negative.
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how do leeuwenhoek’s observations compare to the skin cells and cheek cells you saw in class?
Antonie van Leeuwenhoek was the first to see single-celled organisms. Leeuwenhoek's observations of microorganisms and the development of his own simple microscope, which he used to observe and examine microbial life forms, are significant in the history of microscopy.
His work showed that the microscope was a valuable tool for scientific discovery. Leeuwenhoek's work also established the importance of microorganisms in life processes.A cheek cell is a type of cell that can be seen in human mouths. They appear to be rectangular in shape and have a nucleus in the center. A skin cell is a kind of cell that makes up human skin. It is a type of epithelial cell that is flat and has a nucleus in the center.Both cheek cells and skin cells, on the other hand, are two types of cells that can be seen with a light microscope. Cheek cells and skin cells are much bigger than bacteria, but they are much smaller than the objects Leeuwenhoek saw with his microscope. Leeuwenhoek's discoveries led to the realization that life existed on a small scale, revealing the complexity of even the tiniest forms of life on the planet.
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F=ma During a crash, a dummy with a mass of 60.0 kg hits an airbag that exerts a constant force on the dummy. The acceleration of the dummy is –250 m/s2. What force did the airbag exert on the dummy?
a. -4,170 Newtons
b. -15,000 Newtons
c. -23,500 Newtons
d. 240 Newtons
The force exerted by the airbag on the dummy is -15,000 Newtons.According to Newton's second law of motion, force (F) is equal to mass multiplied by acceleration.
In this scenario, the dummy has a mass of 60.0 kg and experiences an acceleration of -250 [tex]m/s^2[/tex]. Using the formula F = ma, we can calculate the force exerted by the airbag.
Identify the given values:
Mass of the dummy (m) = 60.0 kg
Acceleration of the dummy (a) = -250 [tex]m/s^2[/tex]
Apply the formula F = ma:
Force (F) = 60.0 kg * (-250 [tex]m/s^2[/tex])
Force (F) = -15,000 Newtons
In this scenario, we are given a crash situation where a dummy with a mass of 60.0 kg hits an airbag. We need to determine the force exerted by the airbag on the dummy. To solve this, we can use Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a), expressed as F = ma.
First, we identify the given values. The mass of the dummy is provided as 60.0 kg, and the acceleration experienced by the dummy is -250 [tex]m/s^2[/tex]. The negative sign indicates that the acceleration is in the opposite direction to the positive direction of the coordinate system, implying a deceleration or slowing down of the dummy.
Next, we substitute the values into the formula and calculate the force. Multiplying the mass (60.0 kg) by the acceleration (-250 [tex]m/s^2[/tex]), we find that the force exerted by the airbag on the dummy is -15,000 Newtons. The negative sign indicates that the force is directed opposite to the motion of the dummy, acting as a restraining force to slow it down and protect it during the crash.
To summarize, the airbag exerts a force of -15,000 Newtons on the dummy during the crash. This force is essential in reducing the acceleration of the dummy and providing a cushioning effect, minimizing the potential for injuries.
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Question 3 If the albedo of a planet is 0.2, and the incoming solar radiation is 301 Wm², how much radiation is absorbed by the planet? Round to the nearest whole number (e.g., no decimals) and input
The amount of radiation absorbed by the planet, given an albedo of 0.2 and incoming solar radiation of 301 Wm², is approximately 240 Wm².
What is the amount of radiation absorbed by a planet with an albedo of 0.2 and an incoming solar radiation of 301 Wm²?When solar radiation reaches a planet, a portion of it is reflected back into space, which is determined by the planet's albedo. In this case, the albedo is given as 0.2, meaning that 20% of the incoming radiation is reflected.
To calculate the amount of radiation absorbed, we subtract the reflected radiation from the total incoming radiation.
In this scenario, the incoming solar radiation is 301 Wm². Since the albedo is 0.2, 20% of the radiation is reflected, which is 0.2 * 301 = 60.2 Wm².
To find the absorbed radiation, we subtract the reflected radiation from the total incoming radiation: 301 - 60.2 = 240.8 Wm².
Rounding to the nearest whole number, we get 240 Wm² as the amount of radiation absorbed by the planet.
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A camera lens used for taking close-up photographs has a focal length of 23.5 mm. The farthest it can be placed from the film is 33.0 mm. (a) What is the closest object that can be photographed? (b) What is the magnification of this closest object?
The closest object that can be photographed is 81.63mm and the magnification of this closest object is -0.404.
The focal length of a lens is determined when the lens is focused at infinity. It is obtained from the reciprocal of objects' distance and image distance. Magnification is the enlarged image that is formed over the object size.
From the given,
focal length (f) = 23.5mm
object's distance (u) = 33mm
imagen distance(v) =?
Focal length, (1/f) = 1/u + 1/v
1/v = 1/f - 1/u
=1/23.5 - 1/33
1/v = 12.2mm
v = 1/12.2 mm
= 81.96mm
Thud, the image distance is v= 81.96mm.
Magnification (M) = -v/u
M = -33 / 81.96
= - 0.402.
Thus, the magnification is -0.402.
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when these two metals are placed in contact with one another, which of the following will take place?
When two metals are placed in contact with one another, a galvanic cell is formed. The type of reaction that takes place depends on the metal and the conditions under which they are in contact. The more reactive metal will undergo oxidation while the less reactive metal will undergo reduction.
When two metals are placed in contact with one another, a galvanic cell is formed. The type of reaction that takes place depends on the metal and the conditions under which they are in contact. The more reactive metal will undergo oxidation while the less reactive metal will undergo reduction.The reaction between two metals creates a voltage potential between them. If the potential is high enough, it can cause an electrochemical reaction to take place between the two metals. The flow of electrons through the wire can be harnessed to do work such as powering an electrical device. This phenomenon is the basis for batteries and electrochemical cells.
To conclude, when two metals are placed in contact with one another, a galvanic cell is formed. The type of reaction that takes place depends on the metal and the conditions under which they are in contact. The more reactive metal will undergo oxidation while the less reactive metal will undergo reduction.
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A jewelry designer plans to make some special-ordered silver charms for a commemorative bracelet. If the melting point of silver is 960.8 degrees Celsius, how much heat must the jeweler add to 0.500kg
The amount of heat the jeweler must add to 0.500 kg of silver depends on the initial temperature (T) of the silver.
To calculate the amount of heat the jeweler must add to 0.500 kg of silver in order to raise its temperature to the melting point, we need to use the formula:
Q = mcΔT,
where Q is the heat energy, m is the mass of the substance, c is the specific heat capacity, and ΔT is the change in temperature.
Mass of silver (m): 0.500 kg
Specific heat capacity of silver (c): 0.235 J/g°C (converted to J/kg°C)
Change in temperature (ΔT): The difference between the current temperature of the silver and its melting point.
To raise the temperature of the silver from its current temperature to its melting point, we need to calculate the temperature difference. Let's assume the current temperature is T°C.
ΔT = 960.8°C - T°C
Now we can substitute the values into the formula:
Q = (0.500 kg) * (0.235 J/kg°C) * (960.8°C - T°C)
Therefore, the amount of heat the jeweler must add to 0.500 kg of silver depends on the initial temperature (T) of the silver.
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Two ships, A and B, leave port at the same time. Ship A travels northwest at 24knots, and ship B travels at 28knots in a direction 40 west of south. (1 knot=1 nautical mile per hour; see Appendix D.) What are the
(a) magnitude and
(b) direction of the velocity of ship A relative to B?
(c) After what time will the ships be 160 nautical miles apart?
(d) What will be the bearing of B (the direction of Bs position) relative to A at that time?
(a) Magnitude of the velocity of ship A relative to B= 8 knots(b) Direction of the velocity of ship A relative to B= 298.43 degrees(c) The ships will be 160 nautical miles apart after 5 hours(d) The bearing of B relative to A= 230.25 degrees
Given data,Velocity of ship A = 24 knotsVelocity of ship B = 28 knotsAngle at which ship B is moving= 40 degrees west of south(a) To find magnitude of velocity of ship A relative to B. We will use the relative velocity formula : v^2 = v1^2 + v2^2 - 2v1v2cosθWhere v = relative velocity, v1 = velocity of ship A, v2 = velocity of ship Bθ = angle between the directions of both ships.So, we getv^2 = 24^2 + 28^2 - 2 x 24 x 28 x cos(50)v = 8 knots.Now we will put the value of d as 160 in the above equation, and solve for t.t= 5 hours. On solving, we get : θ = 230.25 degreesTherefore, the bearing of B relative to A= 230.25 degreesAnswer: (a) Magnitude of the velocity of ship A relative to B= 8 knots(b) Direction of the velocity of ship A relative to B= 298.43 degrees(c) The ships will be 160 nautical miles apart after 5 hours(d) The bearing of B relative to A= 230.25 degrees
The given data is,Velocity of ship A = 24 knotsVelocity of ship B = 28 knotsAngle at which ship B is moving= 40 degrees west of south(a) To find magnitude of velocity of ship A relative to B. We will use the relative velocity formula : v^2 = v1^2 + v2^2 - 2v1v2cosθWhere v = relative velocity, v1 = velocity of ship A, v2 = velocity of ship Bθ = angle between the directions of both ships. => θ = 50 degreesSo, we getv^2 = 24^2 + 28^2 - 2 x 24 x 28 x cos(50)v = 8 knotsHence, magnitude of the velocity of ship A relative to B= 8 knots(b) To find direction of velocity of ship A relative to B. We will use the same formula as above:v = √(v1^2 + v2^2 - 2v1v2cosθ)θ = cos^-1[(v1^2 + v2^2 - v^2)/ 2v1v2]θ = cos^-1[(24^2 + 28^2 - 8^2)/ 2 x 24 x 28]θ = 298.43 degreesTherefore, direction of the velocity of ship A relative to B= 298.43 degrees(c) To find after what time will the ships be 160 nautical miles apartWe will use the formula for distance = speed x timeLet time be t. Distance between both the ships after time t, d = √[24tcos45 - (28sin50)t]^2 + [24tsin45 - (28cos50)t]^2d = √[12√2 t - 19.32t]^2 + [12√2t]^2On solving, we get :d = 12t√(33-38cos50)Now we will put the value of d as 160 in the above equation, and solve for t.t= 5 hoursTherefore, after 5 hours the ships will be 160 nautical miles apart.(d) To find bearing of B (the direction of Bs position) relative to A at that time:We will use the formula : tanθ = (sinΔλ) / (cosφ1tanφ2 - sinφ1cosΔλ)Where,φ1 = latitude of A, φ2 = latitude of B,Δλ = difference in longitude of both the ships (40 degrees)On solving, we get : θ = 230.25 degreesTherefore, the bearing of B relative to A= 230.25 degrees.
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what is the earliest time after t = 0 s at which there is a crest at the position x = 3.6 cm ?
To determine the earliest time after t = 0 s at which there is a crest at the position x = 3.6 cm, we need to consider the wave equation for a crest.
The wave equation for a crest is given by:
x = A * cos(2πf(t - T/4))
Where:
x is the position of the wave
A is the amplitude of the wave
f is the frequency of the wave
t is the time
T is the period of the wave
In this case, we are given x = 3.6 cm, and we need to find the earliest time when this position occurs.
To find the earliest time, we can rewrite the wave equation as:
cos(2πf(t - T/4)) = x/A
Taking the inverse cosine of both sides:
2πf(t - T/4) = arccos(x/A)
Simplifying:
t - T/4 = arccos(x/A) / (2πf)
Now, we can solve for t by rearranging the equation:
t = (arccos(x/A) / (2πf)) + T/4
Since we are interested in the earliest time after t = 0 s, we need to find the smallest positive value of t that satisfies the equation.
Plug in the given values:
x = 3.6 cm
A (amplitude) - not given
f (frequency) - not given
T (period) - not given
Without knowing the values for A, f, and T, we cannot calculate the earliest time. We would need additional information about the wave or the specific conditions to determine the values of these variables and calculate the earliest time for a crest at x = 3.6 cm.
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Compute the kinetic energy of a proton (mass 1.67 X 10^-27 kg) using both the nonrelativistic and relativistic expressions for speed of 9.00x10^7m/s Enter your answers numerically separated by a comma. Part B Compute the ratio of the two results (relativistic divided by nonrelativistic) Krel/Knormal=
The relativistic kinetic energy of the proton is 1.89 × 10⁻ⁱ⁴ J.The ratio of relativistic and non-relativistic kinetic energy is 1.04.
Given, mass of the proton, m = 1.67 × 10⁻²⁷ kg
Speed, v = 9.00 × 10⁷ m/sa)
Non-relativistic kinetic energy formula: K = (1/2) m v²
Substitute the values in the above formula to get the non-relativistic kinetic energy of the proton.
K = (1/2) m v²= (1/2) × 1.67 × 10⁻²⁷ × (9.00 × 10⁷)²= 6.76 × 10⁻¹¹ Jb)
Relativistic kinetic energy formula: K = mc² (γ - 1)where γ = 1 / √(1 - v² / c²) is the Lorentz factor.
c is the speed of light, c = 3 × 10⁸ m/s
Substitute the given values in the above formula to get the relativistic kinetic energy of the proton.
K = mc² (γ - 1)= 1.67 × 10⁻²⁷ × (3 × 10⁸)² × [(1 / √(1 - (9.00 × 10⁷)² / (3 × 10⁸)²)) - 1]= 1.89 × 10⁻ⁱ⁴ Jc)
Ratio of the two results:Krel/Knormal= K/Knormal= (mc² (γ - 1)) / (1/2) m v²= 2 × (γ - 1) / v²= 2 × [(1 / √(1 - v² / c²)) - 1] / v²Substitute the given values in the above equation to get the ratio.
Krel/Knormal= K/Knormal= [(2 × [(1 / √(1 - (9.00 × 10⁷)² / (3 × 10⁸)²)) - 1]) / (9.00 × 10⁷)²] / [6.76 × 10⁻¹¹]= 1.04
Approximately, Krel/Knormal = 1.04
The non-relativistic kinetic energy of the proton is 6.76 × 10⁻¹¹ J.
The relativistic kinetic energy of the proton is 1.89 × 10⁻ⁱ⁴ J.The ratio of relativistic and non-relativistic kinetic energy is 1.04.
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measure the coupling constant between he and hf. explain how this can help determine the stereochemistry (i.e. cis vs. trans) of the double bond.
When measuring the coupling constant between he and hf, it can help determine the stereochemistry of the double bond. The coupling constant is the distance between the two peaks in the NMR spectrum. The value of the coupling constant depends on the distance between the two nuclei and the angle between the two bonds connecting the nuclei.
In a cis double bond, the hydrogens (H) are on the same side of the molecule, while in a trans double bond, the hydrogens (H) are on opposite sides of the molecule. When he and hf are in cis double bond, their coupling constant will be larger because the angle between the two bonds connecting the nuclei will be small.In contrast, when he and hf are in a trans double bond, their coupling constant will be smaller because the angle between the two bonds connecting the nuclei will be larger.
The stereochemistry of the double bond can, therefore, be determined based on the value of the coupling constant. In general, if the coupling constant is greater than 10 Hz, it indicates a cis double bond, while if the coupling constant is less than 10 Hz, it indicates a trans double bond.
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A 0.50-mm-diameter hole is illuminated by light of wavelength 500 nm. Part A What is the width (in mm) of the central maximum on a screen 1.6 m behind the slit? W =
To calculate the width of the central maximum on a screen behind the slit, we can use the formula: W = (λ * L) / d
W is the width of the central maximum
λ is the wavelength of light
L is the distance between the slit and the screen
d is the diameter of the hole
λ = 500 nm = 500 × 10^(-9) m
L = 1.6 m
d = 0.50 mm = 0.50 × 10^(-3) m Substituting these values into the formula: W = (500 × 10^(-9) m * 1.6 m) / (0.50 × 10^(-3) m) W = 1.6 × 10^(-6) m To convert the width to millimeters: W = 1.6 × 10^(-6) m * 1000 mm/m. W = 1.6 × 10^(-3) mm. Therefore, the width of the central maximum on the screen is 1.6 × 10^(-3) mm.
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A small comet orbits a heavy star. For each of the following statements, state whether it is true or false. a) The trajectory of the comet is an ellipse with one of the focal points placed very close to the position of the star. b) The amount of time for the comet to go around the star is directly proportional to the cube of the length semi-major axis of the orbit. c) The angular momentum of the comet about the star is constant. d) The linear momentum of the comet is constant. True. This system does not affect by external force
a) The trajectory of the comet an ellipse with one of the focal points placed very close to the position of the star: True
b) The amount of time for the comet to go around the star directly proportional to the cube of the length of the semi-major axis of the orbit: False
c) The angular momentum of the comet about the star constant: True
d) The linear momentum of the comet constant: False
a) True. The trajectory of the comet is indeed an ellipse with one of the focal points placed very close to the position of the star. This is one of the fundamental properties of an elliptical orbit.
b) False. The amount of time for the comet to go around the star is not directly proportional to the cube of the semi-major axis of the orbit.
Instead, it is directly proportional to the 3/2 power of the semi-major axis. This relationship is described by Kepler's third law of planetary motion.
c) True. The angular momentum of the comet about the star is constant. According to the law of conservation of angular momentum, in the absence of external torques, the angular momentum of a system remains constant.
Since there are no external torques acting on the comet-star system, its angular momentum remains constant.
d) False. The linear momentum of the comet is not constant. In an elliptical orbit, the speed of the comet changes as it moves closer to or farther away from the star.
Therefore, the linear momentum, which is the product of mass and velocity, is not constant.
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Question, help with question really appreciated, please only if
you know how to do it, Do part a
A mole of O₂ is compressed from a volume of 21.8 L at 5 °C and 1.75 atm to 15.8 L at the same temperature. Part A Calculate the work done by external forces to compress the gas. = ΑΣΦ ? W = Requ
The work done by external forces to compress the mole of O₂ gas from 21.8 L to 15.8 L at 5 °C and 1.75 atm is approximately 3.9642 atm*L.
To calculate the work done by external forces to compress the gas, we can use the formula:
Work = -PΔV
Where:
P is the pressure
ΔV is the change in volume
First, we need to calculate the initial and final pressures. The initial pressure is given as 1.75 atm, and it remains constant throughout the process since the temperature is kept constant. So, the initial pressure (P1) is 1.75 atm.
To find the final pressure (P2), we can use the ideal gas law equation:
PV = nRT
Where:
P is the pressure
V is the volume
n is the number of moles
R is the ideal gas constant
T is the temperature
P1 = 1.75 atm
V1 = 21.8 L
V2 = 15.8 L
T = 5 °C = 278 K
Rearranging the ideal gas law equation to solve for P2, we have:
P2 = (P1 * V1) / V2
P2 = (1.75 atm * 21.8 L) / 15.8 L
P2 ≈ 2.4107 atm
Now, we can calculate the change in volume:
ΔV = V2 - V1
ΔV = 15.8 L - 21.8 L
ΔV = -6 L
Plugging these values into the work formula:
Work = -(P2 - P1) * ΔV
Work = -(2.4107 atm - 1.75 atm) * -6 L
Work ≈ 3.9642 atm*L
Therefore, the work done by external forces to compress the gas is approximately 3.9642 atm*L.
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QUESTION 6: ELECTRICITY 1 Explain what is meant when a substance is referred to as a bad conductor of electricity and give ONE example. 2 THREE equal resistors are connected in parallel. The total res
When a substance is referred to as a bad conductor of electricity, it means that it does not allow electric current to flow easily through it. This is because the substance has high resistance to the flow of electric charge.
In bad conductors, the electrons are tightly bound to their atoms or molecules, making it difficult for them to move freely and carry the electric current. As a result, only a small amount of current can pass through the substance.
Example: One example of a bad conductor of electricity is rubber. Rubber has high resistance to the flow of electric charge and is commonly used as an insulating material to prevent the flow of current in electrical wires and cables.
2. When three equal resistors are connected in parallel, the total resistance (R_total) of the combination can be calculated using the formula:
1/R_total = 1/R_1 + 1/R_2 + 1/R_3
Where R_1, R_2, and R_3 are the resistances of the individual resistors.
Since the three resistors are equal, the formula simplifies to:
1/R_total = 1/R + 1/R + 1/R = 3/R
We can invert both sides of the equation for value of R_total :
R_total = R/3
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Question 4 Homework. Unanswered Dipole Potential Energy -- What is the minimum potential energy (in Joules) of a q=1.00E-9C dipole with dipole separation of s=1.00E-3m placed in an external electric f
U = Q1 Q2 R. U = 1.00 * 9 * 3m = 27 Joule. Potential energy is the power that a thing possesses as a result of where it is in relation to other objects.
Thus, Potential energy is the power that a thing possesses as a result of where it is in relation to other objects. Because the earth can pull you down through the force of gravity while doing work in the process, being at the top of a stairwell gives you more potential energy than standing at the bottom.
Two magnets have more potential energy when they are held apart than when they are near to one another. They will migrate near each other and begin working.
The force acting on the two objects affects the potential energy formula. P.E. = mgh, where m is the mass in kilograms and g is the acceleration due to gravity, is the formula for gravitational force.
In the given question, U is U = Q1 Q2 R. U = 1.00 * 9 * 3m
= 27 Joule.
Potential energy is the power that a thing possesses as a result of where it is in relation to other objects.
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the rotation of a potter's wheel is started by applying a force of 20n to the edge of the wheel. the wheel has a radius of 20cm. this causes an angular acceleration of 0.75 rad/s^2.
When a force of 20 N is applied to the edge of a wheel that has a radius of 20 cm, it starts rotating. The angular acceleration of the wheel is 0.75 rad/s².Let's see what this means. When a force is applied to an object, it will move, but the movement may not be in the same direction as the force.
If the force is applied at an angle to the object's center of mass, the object will rotate instead of moving in a straight line.The rate at which the rotation occurs is referred to as angular velocity, and it is denoted by the Greek letter omega (ω). Angular acceleration is the rate at which an object's angular velocity changes over time. It is denoted by the Greek letter alpha (α).Using the formula, we can figure out the wheel's angular velocity and how long it takes to reach that velocity. Here's how to go about it:τ = Iα where τ is the torque, I is the moment of inertia, and α is the angular acceleration.We can rearrange this formula to find angular acceleration:
α = τ / I
where α is the angular acceleration, τ is the torque, and I is the moment of inertia.The moment of inertia of a disc (wheel) is ½ MR², where M is the mass and R is the radius. We can determine the torque by multiplying the force by the radius of the wheel, which is 20 cm or 0.2 meters:
τ = F × r
= 20 × 0.2
= 4 NmThe moment of inertia of the wheel is:
I = ½ MR²
= ½ (M × 0.2²)
= 0.02MUsing these values, we can now find the angular acceleration:α = τ / I = 4 / 0.02M
= 200 / M rad/s²If the angular acceleration of the wheel is 0.75 rad/s², we can use this formula to figure out how long it will take to reach that acceleration.t = ω / αwhere t is time and ω is angular velocity.The wheel starts from rest, so its initial angular velocity is zero. Using this formula, we can solve for the time
t = ω / α
= 0.75 / 0.2
= 3.75 seconds.It will take 3.75 seconds for the wheel to reach an angular acceleration of 0.75 rad/s².
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How much work must be done to stop a 1200 kg car traveling at 95 km/h? Express your answer using two significant figures. 17 ΑΣΦ ?
The amount of work required to stop the car is 865,152 J. This work can be done by applying a force over a certain distance, such as by using the brakes or by colliding with another object that can absorb the car's kinetic energy.
To stop a 1200 kg car traveling at 95 km/h, it is necessary to perform work that converts the car's kinetic energy into other forms of energy.
Kinetic energy is the energy that an object possesses as a result of its motion, and is calculated as 1/2 mv^2, where m is the mass of the object and v is its velocity.
To stop the car completely, all of its kinetic energy must be converted into other forms of energy, such as heat, sound, or work done against frictional forces.
The amount of work required to do this is equal to the car's initial kinetic energy, which can be calculated as (1/2)mv^2.In this case, the mass of the car is 1200 kg and its velocity is 95 km/h.
To calculate its kinetic energy, we must first convert the velocity from km/h to m/s:95 km/h = (95/3.6) m/s = 26.4 m/sThen, the kinetic energy of the car can be calculated as:(1/2)(1200 kg)(26.4 m/s)^2= 865,152 J
The actual amount of work required may be greater than this, depending on factors such as the efficiency of the braking system and the amount of frictional forces involved.
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Two m=4.6 g point charges on 1.0-m-long threads repel each other after being charged to q=110 nCas Shown in the figure. (Figure 1) PartA What is the angle You can assume that is a small angle Express your answer to two significant figures and include the appro A 5 4 Value Units
If two m=4.6 g point charges on 1.0-m-long threads repel each other after being charged to q=110 ,the angle between the two point charges would be approximately 54 degrees.
When two point charges repel each other, the force of repulsion acts along the line connecting the charges. In the given scenario, the charges are suspended on 1.0-m-long threads, which implies that the threads are in tension and make a small angle with the vertical.
To find the angle, we can consider the triangle formed by the vertical, the threads, and the line connecting the charges. Since the angle is small, we can approximate the tangent of the angle as the ratio of the vertical displacement (1.0 m) to the horizontal displacement (the distance between the charges).
Using trigonometry, we can calculate the angle as arctan(1.0 m / (0.11 m + 0.11 m)) ≈ 54 degrees.
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Find the y-component of this vector: 42. 2 degrees 101m remember angles are measured from the +x axis
The y-component of the vector with 42.2 degrees 101m is 68.2 m. The y-component of the vector can be found using the formula: y = m sin θ.
To find the y-component of the vector with 42.2 degrees 101m, you need to apply trigonometry concepts. The y-component of the vector can be found using the formula: y = m sin θ, where y is the y-component of the vector, m is the magnitude of the vector, and θ is the angle between the vector and the +x axis.
To apply this formula, first, identify the given angle and the magnitude of the vector. The angle is given as 42.2 degrees, and the magnitude of the vector is given as 101m.
Now, plug in these values into the formula and solve for the y-component:
y = m sin θy
= 101m sin 42.2°y
= 68.2 m (rounded to one decimal place)
Therefore, the y-component of the vector with 42.2 degrees 101m is 68.2 m
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for the last 10 years, the cpi doubled. using the rule of 70, what would be average annual rate of inflation during this time period?
The average annual rate of inflation during this 10-year period would be approximately 7%.
The Rule of 70 states that the approximate doubling time can be calculated by dividing 70 by the annual growth rate. In this case, since the CPI doubled over a 10-year period, we can use the Rule of 70 to find the average annual rate of inflation.
Let's denote the average annual rate of inflation as r.
According to the Rule of 70:
70 / r = 10
Simplifying the equation, we have:
7 = r
Therefore, the average annual rate of inflation during this 10-year period would be approximately 7%.
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what is true when an object is moved closer to a plane mirror?
When an object is moved closer to a plane mirror, its image appears larger but is still the same distance behind the mirror.
A plane mirror produces a virtual image, meaning that the light rays from the object don't actually come together at the location where the image appears to be. When an object is moved closer to a plane mirror, the image appears larger because the angle of incidence and the angle of reflection increase, creating a larger virtual image.
However, the image is still the same distance behind the mirror as it was when the object was farther away, because the distance between the object and the image is twice the distance between the object and the mirror. This is known as the law of reflection and is true for all objects placed in front of a plane mirror, regardless of their distance from the mirror.
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for rayleigh winds with an average wind speed of 8m/s: a. how many hours per year do the winds blow at less than 13 m/s?
The winds blow at less than 13 m/s for approximately 8531.3 hours per year.
For Rayleigh winds with an average wind speed of 8m/s: How many hours per year do the winds blow at less than 13 m/s?The Rayleigh wind speed distribution is described by the equation: f(v) = (v/vm²) * e^(-v²/2vm²), where vm is the most probable velocity (or the maximum of the distribution curve).
1. The probability that a wind speed is less than v is given by: P(v) = ∫ f(v') dv' from 0 to v
For this problem, the average wind speed is 8 m/s. Thus, vm = 1.2 * 8 = 9.6 m/s. The probability that a wind speed is less than 13 m/s can be computed as follows:P(13 m/s) = ∫ f(v') dv' from 0 to 13 = (1/vm²) * ∫ v' * e^(-v²/2vm²) dv' from 0 to 13= 1/9.6² * (-e^(-169/184)) + 13/9.6 * √(2/π) * Erf(13/√(2 * 9.6²))= 0.9743 ≈ 97.43%
Therefore, winds blow at less than 13 m/s for P(13m/s) = 97.43% of the time in a year.
We can calculate the number of hours per year using the following formula: Number of hours = Probability * Number of hours in a year= P(13 m/s) * 8760 hours= 0.9743 * 8760= 8531.3 hours (rounded to one decimal place)
Thus, the winds blow at less than 13 m/s for approximately 8531.3 hours per year.
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10. A 2.5 kg mass is attached to the end of a horizontal spring of spring constant 60 N/m and set into simple harmonic motion with an amplitude of 0.5 m. a. What is the maximum potential energy of the
The maximum potential energy of the mass-spring system is 7.5 Joules. To find the maximum potential energy of the mass-spring system, we can use the formula for potential energy in a spring:
Potential energy (PE) = (1/2) * k * x^2
Where:
PE is the potential energy,
k is the spring constant, and
x is the displacement from the equilibrium position (amplitude in this case).
Mass (m) = 2.5 kg
Spring constant (k) = 60 N/m
Amplitude (A) = 0.5 m
First, we need to find the displacement from the equilibrium position. In simple harmonic motion, the displacement at any point in time can be given by:
x = A * sin(ωt)
Where:
x is the displacement,
A is the amplitude,
ω is the angular frequency (ω = √(k/m)), and
t is the time.
Let's calculate the angular frequency:
ω = √(k/m)
= √(60 N/m / 2.5 kg)
≈ √24 rad/s
≈ 4.899 rad/s
Now, let's find the maximum potential energy:
PE = (1/2) * k * x^2
= (1/2) * 60 N/m * (0.5 m)^2
= (1/2) * 60 N/m * 0.25 m^2
= 7.5 J
Therefore, the maximum potential energy of the mass-spring system is 7.5 Joules.
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The secondary coil of an ideal transformer has 450 turns, and
the primary coil has 75 turns. This type of transformer is a step
down transformer, True or False?
The given statement The secondary coil of an ideal transformer has 450 turns, and the primary coil has 75 turns. This type of transformer is a step down transformer is false.
In a transformer, the turns ratio between the primary and secondary coils determines whether it is a step-up or step-down transformer. The turns ratio is calculated by dividing the number of turns in the secondary coil by the number of turns in the primary coil.
Given that the secondary coil has 450 turns (N₂) and the primary coil has 75 turns (N₁), we can calculate the turns ratio as:
Turns ratio = N₂ / N₁ = 450 / 75 = 6
If the turns ratio is greater than 1, it indicates a step-up transformer, where the voltage is increased from the primary to the secondary coil. Conversely, if the turns ratio is less than 1, it indicates a step-down transformer, where the voltage is decreased from the primary to the secondary coil.
In this case, the turns ratio is 6, which means the secondary voltage will be higher than the primary voltage. Therefore, the given transformer is a step-up transformer, and the statement "This type of transformer is a step down transformer" is false.
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Two parallel, thin, L x L conducting plates are separated by a distance d, as shown. Let L = 2.5 m, and d=2.0 mm. A charge of +4.5 μC is placed on one plate, and a charge of -4.5 μC is placed on the other plate heespertta.com-tracking id 7M79 DS-68-41-BAAS-32165 In accordance with Expert TA's Terms of Service copying this information to solations sharing wabute is strictly forbidden Deing to may result in fimination of your Expert TA Account 50% Part (a) What is the magnitude of charge density on the inside surface of each plate, in coulombs per square meter? A50% Part (b) What is the magnitude of the electric field between the plates?
(a) The magnitude of the charge density on the inside surface of each plate is 1.8 x 10⁴ C/m².
(b) The magnitude of the electric field between the plates is 9 x 10⁶ N/C.
(a) the magnitude of the charge density on the inside surface of each plate, we need to divide the total charge on each plate by the area of that plate. The charge density is given by ρ = Q/A, where ρ is the charge density, Q is the charge, and A is the area. Since the plates are parallel and thin, we can consider them as squares with side length L. Therefore, the area of each plate is A = L².
For each plate, the charge Q is ±4.5 μC. Converting it to coulombs, we have Q = ±4.5 x 10⁻⁶ C. Dividing this by the area, we get ρ = (±4.5 x 10⁻⁶ C) / (2.5 m)².
we find the magnitude of the charge density on the inside surface of each plate to be 1.8 x 10⁴ C/m².
(b) The electric field between the plates can be calculated using the formula E = σ/ε₀, where E is the electric field, σ is the charge density, and ε₀ is the vacuum permittivity. From part (a), we know the charge density is 1.8 x 10⁴ C/m².
The vacuum permittivity ε₀ is approximately 8.85 x 10⁻¹² C²/(N·m²). Plugging in the values, we get E = (1.8 x 10⁴ C/m²) / (8.85 x 10⁻¹² C²/(N·m²)).
we find the magnitude of the electric field between the plates to be approximately 9 x 10⁶ N/C.
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A 0.62 m copper rod with a mass of 0.14 kg carries a current of 12 A in the positive x direction. Let upward be the positive y f5 6/1/22, 10:37 AI What is the magnitude of the minimum magnetic field needed to levitate the rod?
The magnitude of the minimum magnetic field needed to levitate the rod is approximately 0.185 T.
To calculate the magnitude of the minimum magnetic field needed to levitate the copper rod, we can use the equation for the magnetic force on a current-carrying wire: F = BILsin(θ)
Where:
F is the magnetic force
B is the magnetic field
I is the current
L is the length of the wire
θ is the angle between the magnetic field and the current direction
In this case, the copper rod carries a current of 12 A in the positive x direction, and we need to find the minimum magnetic field required to levitate it.
Given:
Length of the rod (L) = 0.62 m
Mass of the rod (m) = 0.14 kg
Current (I) = 12 A
First, let's calculate the magnetic force required to counteract the weight of the rod (assuming the rod is in a uniform magnetic field and the angle θ is 90 degrees, perpendicular to the field):
F = mg
Where:
m is the mass of the rod
g is the acceleration due to gravity (approximately 9.8 m/s^2)
F = (0.14 kg) * (9.8 m/s^2) = 1.372 N
Now, we can rearrange the formula for the magnetic force to solve for the magnetic field (B):
B = F / (ILsin(θ))
Since sin(90 degrees) = 1, we can simplify the equation:
B = F / (IL)
B = 1.372 N / (12 A * 0.62 m)
Using a calculator, the magnitude of the minimum magnetic field needed to levitate the rod is approximately:
B ≈ 0.185 T (tesla)
Therefore, the magnitude of the minimum magnetic field needed to levitate the rod is approximately 0.185 T.
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A piano is tuned by tightening or loosening the piano wires. When the wires are tightened, how is frequency of the waves on the wire affected, if at all? a. The frequency is increased. b. The frequenc
When the piano wires are tightened, the frequency of the waves on the wire is increased. leading to a higher pitch of the sound produced by the piano.
The tension in the piano wires determines the frequency at which the wires vibrate and produce sound. When the wires are tightened, the tension increases, resulting in a higher frequency of vibration and thus a higher pitch of the produced sound. This is because the frequency of a vibrating wire is inversely proportional to its length and directly proportional to the square root of the tension, as given by the equation f = (1/2L) * sqrt(T/m), where f is the frequency, L is the length, T is the tension, and m is the mass per unit length of the wire.
Tightening the piano wires increases the frequency of the waves on the wire, leading to a higher pitch of the sound produced by the piano.
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what effect does an energy change have on the identity of a substance
An energy change can have different effects on the identity of a substance depending on the type of energy involved and the nature of the substance itself. In general, an energy change does not alter the fundamental identity or chemical composition of a substance. The identity of a substance is determined by its unique arrangement of atoms and the types of chemical bonds present.
When considering changes in energy, it is important to distinguish between physical and chemical changes. In a physical change, the substance undergoes a transformation that does not alter its chemical composition. For example, heating water to its boiling point causes a physical change from liquid to gas, but the water molecules remain intact. In this case, the energy change (heat) affects the physical state of the substance but not its identity.
On the other hand, in a chemical change, the substance undergoes a transformation that involves the breaking and forming of chemical bonds, resulting in a different chemical composition. Energy changes, such as heat or light, can drive chemical reactions by providing the necessary activation energy. However, even in a chemical change, the identity of the substance is determined by the arrangement of its atoms and the types of elements involved.
In summary, an energy change, whether in the form of heat, light, or other forms, can affect the physical or chemical properties of a substance, but it does not alter its fundamental identity. The identity of a substance is determined by its unique composition and arrangement of atoms, which remain unchanged during most energy changes.
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