Understanding Gravity - AP Physics C: Electricity and Magnetism
Card 1 of 44
A spherical asteroid has a hole drilled through the center as diagrammed below:
Refer to the diagram above. An object that is much smaller than the asteroid is released from rest at the surface of the asteroid, at point a. How do the velocity and acceleration of the object compare at point b at the surface, and point a, located at the center of the asteroid?
A spherical asteroid has a hole drilled through the center as diagrammed below:
Refer to the diagram above. An object that is much smaller than the asteroid is released from rest at the surface of the asteroid, at point a. How do the velocity and acceleration of the object compare at point b at the surface, and point a, located at the center of the asteroid?
Tap to reveal answer
Because the gravitational force depends only on the mass beneath the object (which is the gravitational version of Gauss's Law for charge), the acceleration steadily decreases as the object falls, and drops to zero at the center. Nevertheless, the velocity keeps increasing as the object falls, it just does so more slowly.
Because the gravitational force depends only on the mass beneath the object (which is the gravitational version of Gauss's Law for charge), the acceleration steadily decreases as the object falls, and drops to zero at the center. Nevertheless, the velocity keeps increasing as the object falls, it just does so more slowly.
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A block with a mass of 
is traveling at 
when it impacts the ground. From how many meters off the ground was the block dropped?
Round to the nearest whole number.
A block with a mass of
Round to the nearest whole number.
Tap to reveal answer
Set the gravitational potential energy and kinetic energy equal to each other and solve for the height.
Mass cancels.
Isolate the height and plug in our values.
Rounding this gives 
.
Set the gravitational potential energy and kinetic energy equal to each other and solve for the height.
Mass cancels.
Isolate the height and plug in our values.
Rounding this gives
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An object of mass 
is dropped from a tower. The object's drag force is given by 
where 
is a positive constant. What will the objects terminal velocity be?
An object of mass
Tap to reveal answer
To find terminal velocity, set the magnitude of the drag force equal to the magnitude of the force of gravity since when these forces are equal and opposite, the object will stop accelerating:
Solve for 
To find terminal velocity, set the magnitude of the drag force equal to the magnitude of the force of gravity since when these forces are equal and opposite, the object will stop accelerating:
Solve for
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A ship of mass 
and an initial velocity of 
is coasting to a stop. The water exerts a drag force on the ship. The drag force is proportional to the velocity:
where the negative sign indicates that the drag force acts in a direction opposite the motion. After the ship has coasted for a time equal to 
, how fast (in terms of 
) will the ship be moving?
A ship of mass
Tap to reveal answer
The ship's equation of velocity (found by solving the first-order differential equation) is 
Substitute 
and solve.
The ship's equation of velocity (found by solving the first-order differential equation) is
Substitute
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A spherical asteroid has a hole drilled through the center as diagrammed below:
Refer to the diagram above. An object that is much smaller than the asteroid is released from rest at the surface of the asteroid, at point a. How do the velocity and acceleration of the object compare at point b at the surface, and point a, located at the center of the asteroid?
A spherical asteroid has a hole drilled through the center as diagrammed below:
Refer to the diagram above. An object that is much smaller than the asteroid is released from rest at the surface of the asteroid, at point a. How do the velocity and acceleration of the object compare at point b at the surface, and point a, located at the center of the asteroid?
Tap to reveal answer
Because the gravitational force depends only on the mass beneath the object (which is the gravitational version of Gauss's Law for charge), the acceleration steadily decreases as the object falls, and drops to zero at the center. Nevertheless, the velocity keeps increasing as the object falls, it just does so more slowly.
Because the gravitational force depends only on the mass beneath the object (which is the gravitational version of Gauss's Law for charge), the acceleration steadily decreases as the object falls, and drops to zero at the center. Nevertheless, the velocity keeps increasing as the object falls, it just does so more slowly.
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A block with a mass of is traveling at when it impacts the ground. From how many meters off the ground was the block dropped?
Round to the nearest whole number.
A block with a mass of
Round to the nearest whole number.
Tap to reveal answer
Set the gravitational potential energy and kinetic energy equal to each other and solve for the height.
Mass cancels.
Isolate the height and plug in our values.
Rounding this gives .
Set the gravitational potential energy and kinetic energy equal to each other and solve for the height.
Mass cancels.
Isolate the height and plug in our values.
Rounding this gives
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An object of mass is dropped from a tower. The object's drag force is given by where is a positive constant. What will the objects terminal velocity be?
An object of mass
Tap to reveal answer
To find terminal velocity, set the magnitude of the drag force equal to the magnitude of the force of gravity since when these forces are equal and opposite, the object will stop accelerating:
Solve for
To find terminal velocity, set the magnitude of the drag force equal to the magnitude of the force of gravity since when these forces are equal and opposite, the object will stop accelerating:
Solve for
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A ship of mass and an initial velocity of is coasting to a stop. The water exerts a drag force on the ship. The drag force is proportional to the velocity:
where the negative sign indicates that the drag force acts in a direction opposite the motion. After the ship has coasted for a time equal to , how fast (in terms of ) will the ship be moving?
A ship of mass
Tap to reveal answer
The ship's equation of velocity (found by solving the first-order differential equation) is
Substitute and solve.
The ship's equation of velocity (found by solving the first-order differential equation) is
Substitute
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A block with a mass of is traveling at when it impacts the ground. From how many meters off the ground was the block dropped?
Round to the nearest whole number.
A block with a mass of
Round to the nearest whole number.
Tap to reveal answer
Set the gravitational potential energy and kinetic energy equal to each other and solve for the height.
Mass cancels.
Isolate the height and plug in our values.
Rounding this gives .
Set the gravitational potential energy and kinetic energy equal to each other and solve for the height.
Mass cancels.
Isolate the height and plug in our values.
Rounding this gives
← Didn't Know|Knew It →
A spherical asteroid has a hole drilled through the center as diagrammed below:
Refer to the diagram above. An object that is much smaller than the asteroid is released from rest at the surface of the asteroid, at point a. How do the velocity and acceleration of the object compare at point b at the surface, and point a, located at the center of the asteroid?
A spherical asteroid has a hole drilled through the center as diagrammed below:
Refer to the diagram above. An object that is much smaller than the asteroid is released from rest at the surface of the asteroid, at point a. How do the velocity and acceleration of the object compare at point b at the surface, and point a, located at the center of the asteroid?
Tap to reveal answer
Because the gravitational force depends only on the mass beneath the object (which is the gravitational version of Gauss's Law for charge), the acceleration steadily decreases as the object falls, and drops to zero at the center. Nevertheless, the velocity keeps increasing as the object falls, it just does so more slowly.
Because the gravitational force depends only on the mass beneath the object (which is the gravitational version of Gauss's Law for charge), the acceleration steadily decreases as the object falls, and drops to zero at the center. Nevertheless, the velocity keeps increasing as the object falls, it just does so more slowly.
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An object of mass is dropped from a tower. The object's drag force is given by where is a positive constant. What will the objects terminal velocity be?
An object of mass
Tap to reveal answer
To find terminal velocity, set the magnitude of the drag force equal to the magnitude of the force of gravity since when these forces are equal and opposite, the object will stop accelerating:
Solve for
To find terminal velocity, set the magnitude of the drag force equal to the magnitude of the force of gravity since when these forces are equal and opposite, the object will stop accelerating:
Solve for
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A ship of mass and an initial velocity of is coasting to a stop. The water exerts a drag force on the ship. The drag force is proportional to the velocity:
where the negative sign indicates that the drag force acts in a direction opposite the motion. After the ship has coasted for a time equal to , how fast (in terms of ) will the ship be moving?
A ship of mass
Tap to reveal answer
The ship's equation of velocity (found by solving the first-order differential equation) is
Substitute and solve.
The ship's equation of velocity (found by solving the first-order differential equation) is
Substitute
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A block with a mass of is traveling at when it impacts the ground. From how many meters off the ground was the block dropped?
Round to the nearest whole number.
A block with a mass of
Round to the nearest whole number.
Tap to reveal answer
Set the gravitational potential energy and kinetic energy equal to each other and solve for the height.
Mass cancels.
Isolate the height and plug in our values.
Rounding this gives .
Set the gravitational potential energy and kinetic energy equal to each other and solve for the height.
Mass cancels.
Isolate the height and plug in our values.
Rounding this gives
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A spherical asteroid has a hole drilled through the center as diagrammed below:
Refer to the diagram above. An object that is much smaller than the asteroid is released from rest at the surface of the asteroid, at point a. How do the velocity and acceleration of the object compare at point b at the surface, and point a, located at the center of the asteroid?
A spherical asteroid has a hole drilled through the center as diagrammed below:
Refer to the diagram above. An object that is much smaller than the asteroid is released from rest at the surface of the asteroid, at point a. How do the velocity and acceleration of the object compare at point b at the surface, and point a, located at the center of the asteroid?
Tap to reveal answer
Because the gravitational force depends only on the mass beneath the object (which is the gravitational version of Gauss's Law for charge), the acceleration steadily decreases as the object falls, and drops to zero at the center. Nevertheless, the velocity keeps increasing as the object falls, it just does so more slowly.
Because the gravitational force depends only on the mass beneath the object (which is the gravitational version of Gauss's Law for charge), the acceleration steadily decreases as the object falls, and drops to zero at the center. Nevertheless, the velocity keeps increasing as the object falls, it just does so more slowly.
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An object of mass is dropped from a tower. The object's drag force is given by where is a positive constant. What will the objects terminal velocity be?
An object of mass
Tap to reveal answer
To find terminal velocity, set the magnitude of the drag force equal to the magnitude of the force of gravity since when these forces are equal and opposite, the object will stop accelerating:
Solve for
To find terminal velocity, set the magnitude of the drag force equal to the magnitude of the force of gravity since when these forces are equal and opposite, the object will stop accelerating:
Solve for
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A ship of mass and an initial velocity of is coasting to a stop. The water exerts a drag force on the ship. The drag force is proportional to the velocity:
where the negative sign indicates that the drag force acts in a direction opposite the motion. After the ship has coasted for a time equal to , how fast (in terms of ) will the ship be moving?
A ship of mass
Tap to reveal answer
The ship's equation of velocity (found by solving the first-order differential equation) is
Substitute and solve.
The ship's equation of velocity (found by solving the first-order differential equation) is
Substitute
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A block with a mass of is traveling at when it impacts the ground. From how many meters off the ground was the block dropped?
Round to the nearest whole number.
A block with a mass of
Round to the nearest whole number.
Tap to reveal answer
Set the gravitational potential energy and kinetic energy equal to each other and solve for the height.
Mass cancels.
Isolate the height and plug in our values.
Rounding this gives .
Set the gravitational potential energy and kinetic energy equal to each other and solve for the height.
Mass cancels.
Isolate the height and plug in our values.
Rounding this gives
← Didn't Know|Knew It →
A spherical asteroid has a hole drilled through the center as diagrammed below:
Refer to the diagram above. An object that is much smaller than the asteroid is released from rest at the surface of the asteroid, at point a. How do the velocity and acceleration of the object compare at point b at the surface, and point a, located at the center of the asteroid?
A spherical asteroid has a hole drilled through the center as diagrammed below:
Refer to the diagram above. An object that is much smaller than the asteroid is released from rest at the surface of the asteroid, at point a. How do the velocity and acceleration of the object compare at point b at the surface, and point a, located at the center of the asteroid?
Tap to reveal answer
Because the gravitational force depends only on the mass beneath the object (which is the gravitational version of Gauss's Law for charge), the acceleration steadily decreases as the object falls, and drops to zero at the center. Nevertheless, the velocity keeps increasing as the object falls, it just does so more slowly.
Because the gravitational force depends only on the mass beneath the object (which is the gravitational version of Gauss's Law for charge), the acceleration steadily decreases as the object falls, and drops to zero at the center. Nevertheless, the velocity keeps increasing as the object falls, it just does so more slowly.
← Didn't Know|Knew It →
An object of mass is dropped from a tower. The object's drag force is given by where is a positive constant. What will the objects terminal velocity be?
An object of mass
Tap to reveal answer
To find terminal velocity, set the magnitude of the drag force equal to the magnitude of the force of gravity since when these forces are equal and opposite, the object will stop accelerating:
Solve for
To find terminal velocity, set the magnitude of the drag force equal to the magnitude of the force of gravity since when these forces are equal and opposite, the object will stop accelerating:
Solve for
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A ship of mass and an initial velocity of is coasting to a stop. The water exerts a drag force on the ship. The drag force is proportional to the velocity:
where the negative sign indicates that the drag force acts in a direction opposite the motion. After the ship has coasted for a time equal to , how fast (in terms of ) will the ship be moving?
A ship of mass
Tap to reveal answer
The ship's equation of velocity (found by solving the first-order differential equation) is
Substitute and solve.
The ship's equation of velocity (found by solving the first-order differential equation) is
Substitute
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