# AP Physics 1 : Specific Forces

## Example Questions

### Example Question #81 : Specific Forces

The center of the moon is  from the earth.

The earth has a mass of .

Estimate lunar velocity.

Possible Answers:

None of these

Correct answer:

Explanation:

In an orbit, the centripital force will be equal to the gravitational force:

Where:

is the distance to the center of the earth from the center of the moon.

is the linear velocity of the moon

is the mass of the moon

is the mass of the earth

is the universal gravity constant,

Simplifying and plugging in values:

Solving for :

*note how the mass of the moon was irrelevant

### Example Question #82 : Specific Forces

Earth radius:

Earth mass:

Gravity constant:

A space ship is in a perfectly circular orbit above the earth. Determine it's linear velocity.

Possible Answers:

Correct answer:

Explanation:

In orbit, the magnitude of the centripetal force is in magnitude equal to the gravitational force:

Where is the linear velocity and is the distance from the center of the earth.

Solve for :

Plug in values:

### Example Question #83 : Specific Forces

Distance from earth to the moon:

Mass of moon:

Universal gravitation constant:

Estimate the gravitational force of the moon on a person of mass on the surface of the earth.

Possible Answers:

Correct answer:

Explanation:

Use the law of universal gravitation:

Convert  to and plug in values:

### Example Question #81 : Forces

Mass of moon:

Moon radius:

A spacecraft is orbiting above the surface of the moon. Determine the velocity of the spacecraft.

Possible Answers:

Correct answer:

Explanation:

In an orbit, the centripetal force will be equal to the gravitational force:

Where:

is the distance to the moon's center. This will be the sum of the radius of the moon and the distance above the moon's center

is the linear velocity

is the mass of the ship

is the mass of the moon

is the universal gravity constant,

Simplify and plug in values:

Solve for :

### Example Question #85 : Specific Forces

Mass of Earth:

Mass of Moon:

Distance between Earth and Moon:

If a spaceship were to travel in a straight line towards the moon, at approximately what distance from the Earth would the forces of gravity due to the earth and moon be equal in magnitude?

Possible Answers:

None of these

Correct answer:

Explanation:

Use the following equations to set up our calculation:

Combine equations and simplify:

Plug in values:

Solve for by converting to a quadratic equation:

Use the quadratic formula to solve:

### Example Question #81 : Forces

Pluto radius:

Pluto mass:

Determine the gravity constant,  on the surface of Pluto.

Possible Answers:

Correct answer:

Explanation:

Set both forms of gravitational force equal to each other.

Simplify:

Plug in values:

### Example Question #41 : Universal Gravitation

How would the linear velocity of the Moon be different if it's mass was doubled? Assume that the distance to the Earth stayed the same.

Possible Answers:

Unchanged

Quadrupled

Doubled

Quartered

Halved

Correct answer:

Unchanged

Explanation:

Set centripetal force equal to gravitational force:

The mass of the Moon, cancels out, thus, there is no effect.

### Example Question #82 : Forces

If on earth you have a weight, , what would your new weight be if you were standing on a planet with the same mass as earth, but with half the radius?

Possible Answers:

your earth weight.

times your earth weight

times your earth weight.

The same as your earth weight.

your earth weight.

Correct answer:

times your earth weight.

Explanation:

Your weight is a function of how much force is pulling you down towards the planet, not just your mass.  To find force when your standing on a different planet, you would need to use Newton's Law of Universal Gravitation.

To compare the forces from each planet, you would set this equation equal to itself.

We then cancel the common terms, in this formula that's the negative sign,  (the gravitational constant), and the mass of the earth/planet (because they're the same).  After that we can substitute the radius of the new planet for half of the earth radius.

We need to remember that when we square the radius in the Law of Universal Gravitation, we also need to square the , making it .  Because the  is in the denominator, we take the inverse of it, so you would feel  times more force standing on the new planet.  Therefore you would have  times as much weight.

### Example Question #89 : Specific Forces

An electronic scale is used to find the mass of a lead cube at sea level. The scale and lead cube are then transported to the top of a mountain, over  above sea level. How does the weight reading compare to the weight given at sea level?

Possible Answers:

It will be smaller

It will be the same

It will be larger

None of these

It is impossible to determine

Correct answer:

It will be smaller

Explanation:

The electronic scale measures based on the normal force the scale provides to the object. This in turn is based on the force of gravity on the object by the earth.

As height above sea level increases, as does , the distance to the center of the Earth. As  increases,  decreases. This would decrease the normal force which would decrease the reading on the scale.

### Example Question #90 : Specific Forces

Mass of moon:

Radius of moon:

A spring of rest length is placed upright on the moon. A mass of is gently placed on top and the spring contracts by . Determine the spring constant.

Possible Answers:

None of these

Correct answer:

Explanation:

First, estimate the acceleration due to gravity close to the moon's surface:

Combining equations and solving for the acceleration:

Converting to and pugging in values:

Using

Solving for

Converting to and plugging in values:

(Since the mass is at rest, the acceleration and thus the net force is zero)