Calculating Gravitational Forces - AP Physics C: Electricity and Magnetism
Card 1 of 66
With what minimum velocity must a rocket be launched from the surface of the moon in order to not fall back down due to the moon's gravity?
The mass of the moon is 
and its radius is 
.
With what minimum velocity must a rocket be launched from the surface of the moon in order to not fall back down due to the moon's gravity?
The mass of the moon is
Tap to reveal answer
Relevant equations:
For the rocket to escape the moon's gravity, its minimum total energy is zero. If the total energy is zero, the rocket will have zero final velocity when it is infinitely far from the moon. If total energy is less than zero, the rocket will fall back to the moon's surface. If total energy is greater than zero, the rocket will have some final velocity when it is infinitely far away.
For the minimum energy case as the rocket leaves the surface:
Rearrange energy equation to isolate the velocity term.
Substitute in the given values to solve for the velocity.
Relevant equations:
For the rocket to escape the moon's gravity, its minimum total energy is zero. If the total energy is zero, the rocket will have zero final velocity when it is infinitely far from the moon. If total energy is less than zero, the rocket will fall back to the moon's surface. If total energy is greater than zero, the rocket will have some final velocity when it is infinitely far away.
For the minimum energy case as the rocket leaves the surface:
Rearrange energy equation to isolate the velocity term.
Substitute in the given values to solve for the velocity.
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What is the gravitational force of the sun on a 
book on the earth's surface if the sun's mass is 
and the earth-sun distance is 
?
What is the gravitational force of the sun on a
Tap to reveal answer
Relevant equations:
Use the given values to solve for the force.
Relevant equations:
Use the given values to solve for the force.
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Two spheres of equal mass are isolated in space, and are separated by a distance 
. If that distance is doubled, by what factor does the gravitational force between the two spheres change?
Two spheres of equal mass are isolated in space, and are separated by a distance
Tap to reveal answer
Newton's law of universal gravitation states:
We can write two equations for the gravity experienced before and after the doubling:
The equation for gravity after the doubling can be simplified:
Because the masses of the spheres remain the same, as does the universal gravitation constant, we can substitute the definition of Fg1 into that equation:
The the gravitational force decreases by a factor of 4 when the distance between the two spheres is doubled.
Newton's law of universal gravitation states:
We can write two equations for the gravity experienced before and after the doubling:
The equation for gravity after the doubling can be simplified:
Because the masses of the spheres remain the same, as does the universal gravitation constant, we can substitute the definition of Fg1 into that equation:
The the gravitational force decreases by a factor of 4 when the distance between the two spheres is doubled.
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Two spheres of equal mass are isolated in space. If the mass of one sphere is doubled, by what factor does the gravitational force experienced by the two spheres change?
Two spheres of equal mass are isolated in space. If the mass of one sphere is doubled, by what factor does the gravitational force experienced by the two spheres change?
Tap to reveal answer
Newton's law of universal gravitation states that:
We can write two equations representing the force of gravity before and after the doubling of the mass:
The problem gives us 
and we can assume that all other variables stay constant.
Substituting these defintions into the second equation:
This equation simplifies to:
Substituting the definition of Fg1, we see:
Thus the gravitational forces doubles when the mass of one object doubles.
Newton's law of universal gravitation states that:
We can write two equations representing the force of gravity before and after the doubling of the mass:
The problem gives us
Substituting these defintions into the second equation:
This equation simplifies to:
Substituting the definition of Fg1, we see:
Thus the gravitational forces doubles when the mass of one object doubles.
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You are riding in an elevator that is accelerating upwards at 
, when you note that a block suspended vertically from a spring scale gives a reading of 
.
What does the spring scale read when the elevator is descending at constant speed?
You are riding in an elevator that is accelerating upwards at
What does the spring scale read when the elevator is descending at constant speed?
Tap to reveal answer
When the elevator accelerates upward, we know that an object would appear heavier. The normal force is the sum of all the forces added up, and in this case it is 
. We know that the normal force has two components, a component from gravity, and a component from the acceleration of the elevator. Using this equation, we can determine the mass of the block, which doesn't change:
is acceleration due to gravity and 
is the acceleration of the elevator.
When substituting in the values, we get 
Solving for 
, we get 
Since the elevator is descending at constant speed, no additional force is applied, therefore the force that the spring scale reads is only due to gravity, which is calculated by:
When the elevator accelerates upward, we know that an object would appear heavier. The normal force is the sum of all the forces added up, and in this case it is
When substituting in the values, we get
Solving for
Since the elevator is descending at constant speed, no additional force is applied, therefore the force that the spring scale reads is only due to gravity, which is calculated by:
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The mass and radius of a planet’s moon are 
and 
respectively.
With what minimum speed would a bullet have to be fired horizontally near the surface of this moon in order for it to never hit the ground?
(Note: You can treat the moon as a smooth sphere, and assume there’s no atmosphere.)
The mass and radius of a planet’s moon are
With what minimum speed would a bullet have to be fired horizontally near the surface of this moon in order for it to never hit the ground?
(Note: You can treat the moon as a smooth sphere, and assume there’s no atmosphere.)
Tap to reveal answer
To do this problem we have to realize that the force of gravity acting on the bullet is equal to the centripetal force. The equations for gravitational force and centripetal force are as follows:
If we set the two equations equal to each other, the small 
(mass of the bullet) will cancel out and 
will disappear from the right side of the equation.
is the universal gravitational constant 
is given to be 
and 
to be 
.
If we plug everything in, we get
or 
To do this problem we have to realize that the force of gravity acting on the bullet is equal to the centripetal force. The equations for gravitational force and centripetal force are as follows:
If we set the two equations equal to each other, the small
If we plug everything in, we get
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With what minimum velocity must a rocket be launched from the surface of the moon in order to not fall back down due to the moon's gravity?
The mass of the moon is and its radius is .
With what minimum velocity must a rocket be launched from the surface of the moon in order to not fall back down due to the moon's gravity?
The mass of the moon is
Tap to reveal answer
Relevant equations:
For the rocket to escape the moon's gravity, its minimum total energy is zero. If the total energy is zero, the rocket will have zero final velocity when it is infinitely far from the moon. If total energy is less than zero, the rocket will fall back to the moon's surface. If total energy is greater than zero, the rocket will have some final velocity when it is infinitely far away.
For the minimum energy case as the rocket leaves the surface:
Rearrange energy equation to isolate the velocity term.
Substitute in the given values to solve for the velocity.
Relevant equations:
For the rocket to escape the moon's gravity, its minimum total energy is zero. If the total energy is zero, the rocket will have zero final velocity when it is infinitely far from the moon. If total energy is less than zero, the rocket will fall back to the moon's surface. If total energy is greater than zero, the rocket will have some final velocity when it is infinitely far away.
For the minimum energy case as the rocket leaves the surface:
Rearrange energy equation to isolate the velocity term.
Substitute in the given values to solve for the velocity.
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What is the gravitational force of the sun on a book on the earth's surface if the sun's mass is and the earth-sun distance is ?
What is the gravitational force of the sun on a
Tap to reveal answer
Relevant equations:
Use the given values to solve for the force.
Relevant equations:
Use the given values to solve for the force.
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Two spheres of equal mass are isolated in space, and are separated by a distance . If that distance is doubled, by what factor does the gravitational force between the two spheres change?
Two spheres of equal mass are isolated in space, and are separated by a distance
Tap to reveal answer
Newton's law of universal gravitation states:
We can write two equations for the gravity experienced before and after the doubling:
The equation for gravity after the doubling can be simplified:
Because the masses of the spheres remain the same, as does the universal gravitation constant, we can substitute the definition of Fg1 into that equation:
The the gravitational force decreases by a factor of 4 when the distance between the two spheres is doubled.
Newton's law of universal gravitation states:
We can write two equations for the gravity experienced before and after the doubling:
The equation for gravity after the doubling can be simplified:
Because the masses of the spheres remain the same, as does the universal gravitation constant, we can substitute the definition of Fg1 into that equation:
The the gravitational force decreases by a factor of 4 when the distance between the two spheres is doubled.
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Two spheres of equal mass are isolated in space. If the mass of one sphere is doubled, by what factor does the gravitational force experienced by the two spheres change?
Two spheres of equal mass are isolated in space. If the mass of one sphere is doubled, by what factor does the gravitational force experienced by the two spheres change?
Tap to reveal answer
Newton's law of universal gravitation states that:
We can write two equations representing the force of gravity before and after the doubling of the mass:
The problem gives us and we can assume that all other variables stay constant.
Substituting these defintions into the second equation:
This equation simplifies to:
Substituting the definition of Fg1, we see:
Thus the gravitational forces doubles when the mass of one object doubles.
Newton's law of universal gravitation states that:
We can write two equations representing the force of gravity before and after the doubling of the mass:
The problem gives us
Substituting these defintions into the second equation:
This equation simplifies to:
Substituting the definition of Fg1, we see:
Thus the gravitational forces doubles when the mass of one object doubles.
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You are riding in an elevator that is accelerating upwards at , when you note that a block suspended vertically from a spring scale gives a reading of .
What does the spring scale read when the elevator is descending at constant speed?
You are riding in an elevator that is accelerating upwards at
What does the spring scale read when the elevator is descending at constant speed?
Tap to reveal answer
When the elevator accelerates upward, we know that an object would appear heavier. The normal force is the sum of all the forces added up, and in this case it is . We know that the normal force has two components, a component from gravity, and a component from the acceleration of the elevator. Using this equation, we can determine the mass of the block, which doesn't change:
is acceleration due to gravity and is the acceleration of the elevator.
When substituting in the values, we get
Solving for , we get
Since the elevator is descending at constant speed, no additional force is applied, therefore the force that the spring scale reads is only due to gravity, which is calculated by:
When the elevator accelerates upward, we know that an object would appear heavier. The normal force is the sum of all the forces added up, and in this case it is
When substituting in the values, we get
Solving for
Since the elevator is descending at constant speed, no additional force is applied, therefore the force that the spring scale reads is only due to gravity, which is calculated by:
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The mass and radius of a planet’s moon are and respectively.
With what minimum speed would a bullet have to be fired horizontally near the surface of this moon in order for it to never hit the ground?
(Note: You can treat the moon as a smooth sphere, and assume there’s no atmosphere.)
The mass and radius of a planet’s moon are
With what minimum speed would a bullet have to be fired horizontally near the surface of this moon in order for it to never hit the ground?
(Note: You can treat the moon as a smooth sphere, and assume there’s no atmosphere.)
Tap to reveal answer
To do this problem we have to realize that the force of gravity acting on the bullet is equal to the centripetal force. The equations for gravitational force and centripetal force are as follows:
If we set the two equations equal to each other, the small (mass of the bullet) will cancel out and will disappear from the right side of the equation.
is the universal gravitational constant
is given to be and to be .
If we plug everything in, we get
or
To do this problem we have to realize that the force of gravity acting on the bullet is equal to the centripetal force. The equations for gravitational force and centripetal force are as follows:
If we set the two equations equal to each other, the small
If we plug everything in, we get
← Didn't Know|Knew It →
With what minimum velocity must a rocket be launched from the surface of the moon in order to not fall back down due to the moon's gravity?
The mass of the moon is and its radius is .
With what minimum velocity must a rocket be launched from the surface of the moon in order to not fall back down due to the moon's gravity?
The mass of the moon is
Tap to reveal answer
Relevant equations:
For the rocket to escape the moon's gravity, its minimum total energy is zero. If the total energy is zero, the rocket will have zero final velocity when it is infinitely far from the moon. If total energy is less than zero, the rocket will fall back to the moon's surface. If total energy is greater than zero, the rocket will have some final velocity when it is infinitely far away.
For the minimum energy case as the rocket leaves the surface:
Rearrange energy equation to isolate the velocity term.
Substitute in the given values to solve for the velocity.
Relevant equations:
For the rocket to escape the moon's gravity, its minimum total energy is zero. If the total energy is zero, the rocket will have zero final velocity when it is infinitely far from the moon. If total energy is less than zero, the rocket will fall back to the moon's surface. If total energy is greater than zero, the rocket will have some final velocity when it is infinitely far away.
For the minimum energy case as the rocket leaves the surface:
Rearrange energy equation to isolate the velocity term.
Substitute in the given values to solve for the velocity.
← Didn't Know|Knew It →
What is the gravitational force of the sun on a book on the earth's surface if the sun's mass is and the earth-sun distance is ?
What is the gravitational force of the sun on a
Tap to reveal answer
Relevant equations:
Use the given values to solve for the force.
Relevant equations:
Use the given values to solve for the force.
← Didn't Know|Knew It →
Two spheres of equal mass are isolated in space, and are separated by a distance . If that distance is doubled, by what factor does the gravitational force between the two spheres change?
Two spheres of equal mass are isolated in space, and are separated by a distance
Tap to reveal answer
Newton's law of universal gravitation states:
We can write two equations for the gravity experienced before and after the doubling:
The equation for gravity after the doubling can be simplified:
Because the masses of the spheres remain the same, as does the universal gravitation constant, we can substitute the definition of Fg1 into that equation:
The the gravitational force decreases by a factor of 4 when the distance between the two spheres is doubled.
Newton's law of universal gravitation states:
We can write two equations for the gravity experienced before and after the doubling:
The equation for gravity after the doubling can be simplified:
Because the masses of the spheres remain the same, as does the universal gravitation constant, we can substitute the definition of Fg1 into that equation:
The the gravitational force decreases by a factor of 4 when the distance between the two spheres is doubled.
← Didn't Know|Knew It →
Two spheres of equal mass are isolated in space. If the mass of one sphere is doubled, by what factor does the gravitational force experienced by the two spheres change?
Two spheres of equal mass are isolated in space. If the mass of one sphere is doubled, by what factor does the gravitational force experienced by the two spheres change?
Tap to reveal answer
Newton's law of universal gravitation states that:
We can write two equations representing the force of gravity before and after the doubling of the mass:
The problem gives us and we can assume that all other variables stay constant.
Substituting these defintions into the second equation:
This equation simplifies to:
Substituting the definition of Fg1, we see:
Thus the gravitational forces doubles when the mass of one object doubles.
Newton's law of universal gravitation states that:
We can write two equations representing the force of gravity before and after the doubling of the mass:
The problem gives us
Substituting these defintions into the second equation:
This equation simplifies to:
Substituting the definition of Fg1, we see:
Thus the gravitational forces doubles when the mass of one object doubles.
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You are riding in an elevator that is accelerating upwards at , when you note that a block suspended vertically from a spring scale gives a reading of .
What does the spring scale read when the elevator is descending at constant speed?
You are riding in an elevator that is accelerating upwards at
What does the spring scale read when the elevator is descending at constant speed?
Tap to reveal answer
When the elevator accelerates upward, we know that an object would appear heavier. The normal force is the sum of all the forces added up, and in this case it is . We know that the normal force has two components, a component from gravity, and a component from the acceleration of the elevator. Using this equation, we can determine the mass of the block, which doesn't change:
is acceleration due to gravity and is the acceleration of the elevator.
When substituting in the values, we get
Solving for , we get
Since the elevator is descending at constant speed, no additional force is applied, therefore the force that the spring scale reads is only due to gravity, which is calculated by:
When the elevator accelerates upward, we know that an object would appear heavier. The normal force is the sum of all the forces added up, and in this case it is
When substituting in the values, we get
Solving for
Since the elevator is descending at constant speed, no additional force is applied, therefore the force that the spring scale reads is only due to gravity, which is calculated by:
← Didn't Know|Knew It →
The mass and radius of a planet’s moon are and respectively.
With what minimum speed would a bullet have to be fired horizontally near the surface of this moon in order for it to never hit the ground?
(Note: You can treat the moon as a smooth sphere, and assume there’s no atmosphere.)
The mass and radius of a planet’s moon are
With what minimum speed would a bullet have to be fired horizontally near the surface of this moon in order for it to never hit the ground?
(Note: You can treat the moon as a smooth sphere, and assume there’s no atmosphere.)
Tap to reveal answer
To do this problem we have to realize that the force of gravity acting on the bullet is equal to the centripetal force. The equations for gravitational force and centripetal force are as follows:
If we set the two equations equal to each other, the small (mass of the bullet) will cancel out and will disappear from the right side of the equation.
is the universal gravitational constant
is given to be and to be .
If we plug everything in, we get
or
To do this problem we have to realize that the force of gravity acting on the bullet is equal to the centripetal force. The equations for gravitational force and centripetal force are as follows:
If we set the two equations equal to each other, the small
If we plug everything in, we get
← Didn't Know|Knew It →
With what minimum velocity must a rocket be launched from the surface of the moon in order to not fall back down due to the moon's gravity?
The mass of the moon is and its radius is .
With what minimum velocity must a rocket be launched from the surface of the moon in order to not fall back down due to the moon's gravity?
The mass of the moon is
Tap to reveal answer
Relevant equations:
For the rocket to escape the moon's gravity, its minimum total energy is zero. If the total energy is zero, the rocket will have zero final velocity when it is infinitely far from the moon. If total energy is less than zero, the rocket will fall back to the moon's surface. If total energy is greater than zero, the rocket will have some final velocity when it is infinitely far away.
For the minimum energy case as the rocket leaves the surface:
Rearrange energy equation to isolate the velocity term.
Substitute in the given values to solve for the velocity.
Relevant equations:
For the rocket to escape the moon's gravity, its minimum total energy is zero. If the total energy is zero, the rocket will have zero final velocity when it is infinitely far from the moon. If total energy is less than zero, the rocket will fall back to the moon's surface. If total energy is greater than zero, the rocket will have some final velocity when it is infinitely far away.
For the minimum energy case as the rocket leaves the surface:
Rearrange energy equation to isolate the velocity term.
Substitute in the given values to solve for the velocity.
← Didn't Know|Knew It →
What is the gravitational force of the sun on a book on the earth's surface if the sun's mass is and the earth-sun distance is ?
What is the gravitational force of the sun on a
Tap to reveal answer
Relevant equations:
Use the given values to solve for the force.
Relevant equations:
Use the given values to solve for the force.
← Didn't Know|Knew It →