### All AP Physics 1 Resources

## Example Questions

### Example Question #31 : Understanding Universal Gravitation

A satellite orbits above the Earth. The satellite runs into another stationary satellite of equal mass and the two stick together. What is their resulting velocity?

**Possible Answers:**

**Correct answer:**

We can use the conservation of momentum to solve. Since the satellites stick together, there is only one final velocity term.

We know the masses for both satellites are equal, and the second satellite is initially stationary.

Now we need to find the velocity of the first satellite. Since the satellite is in orbit (circular motion), we need to find the tangential velocity. We can do this by finding the centripetal acceleration from the centripetal force.

Recognize that the force due to gravity of the Earth on the satellite is the same as the centripetal force acting on the satellite. That means .

Solve for for the satellite. To do this, use the law of universal gravitation.

Remember that is the distance between the centers of the two objects. That means it will be equal to the radius of the earth PLUS the orbiting distance.

Use the given values for the masses of the objects and distance to solve for the force of gravity.

Now that we know the force, we can find the acceleration. Remember that centripetal force is . Set our two forces equal and solve for the centripetal acceleration.

Now we can find the tangential velocity, using the equation for centripetal acceleration. Again, remember that the radius is equal to the sum of the radius of the Earth and the height of the satellite!

This value is the tangential velocity, or the initial velocity of the first satellite. We can plug this into the equation for conversation of momentum to solve for the final velocity of the two satellites.

### Example Question #72 : Forces

A satellite orbits above the Earth. What is the period of the satellite's orbit?

**Possible Answers:**

**Correct answer:**

The period describes how long it takes the satellite to make one full orbit. If you go back to the definition of velocity, , we can apply that to our new circular orbit, in which the distance is equal to the circumference of the circle and the time is equal to the period: . The circumference divided by the period will give us the average velocity.

The problem gives us the radius, but we need to find the tangential velocity. We can do this by first solving for the centripetal acceleration from the centripetal force.

Recognize that the force due to gravity of the Earth on the satellite is the same as the centripetal force acting on the satellite. That means .

Solve for for the satellite. To do this, use the law of universal gravitation.

Remember that is the distance between the centers of the two objects. That means it will be equal to the radius of the earth PLUS the orbiting distance.

Use the given values for the masses of the objects and distance to solve for the force of gravity.

Now that we know the force, we can find the acceleration. Remember that centripetal force is . Set our two forces equal and solve for the centripetal acceleration.

Now we can find the tangential velocity, using the equation for centripetal acceleration. Again, remember that the radius is equal to the sum of the radius of the Earth and the height of the satellite!

We now have a value for the tangential velocity, which we can use in the equation for velocity from the beginning to find the period.

### Example Question #81 : Forces

Two planets are apart. If the first planet has a mass of and the second has a mass of , what is the gravitational force between them?

**Possible Answers:**

**Correct answer:**

To solve, use Newton's law of universal gravitation:

We are given the values for the mass of each planet, as well as the distance (radius) between them. Using these values and the gravitational constant, we can solve for the force of gravity.

### Example Question #31 : Universal Gravitation

Two planets are apart. If the first planet has a mass of and the second has a mass of , what is the acceleration on the smaller planet?

**Possible Answers:**

**Correct answer:**

Remember that Newton's second law states that . The force acting upon the planet in question will be the force due to gravity. Once we find that, we can find the acceleration.

To solve for the force, use Newton's law of universal gravitation:

We are given the values for the mass of each planet, as well as the distance (radius) between them. Using these values and the gravitational constant, we can solve for the force of gravity.

Now that we know the force of gravity, we can use Newton's second law and the mass of the smaller planet to solve for the acceleration of gravity.### Example Question #31 : Universal Gravitation

Two planets are apart. If the first planet has a mass of and the second has a mass of , what is the acceleration on the larger planet?

**Possible Answers:**

**Correct answer:**

Remember that Newton's second law states that . The force acting upon the planet in question will be the force due to gravity. Once we find that, we can find the acceleration.

To solve for the force, use Newton's law of universal gravitation:

We are given the values for the mass of each planet, as well as the distance (radius) between them. Using these values and the gravitational constant, we can solve for the force of gravity.

Now that we know the force of gravity, we can use Newton's second law and the mass of the larger planet to solve for the acceleration of gravity.### Example Question #76 : Forces

An astronaut has a mass of . He travels to a new planet and observes his weight is on this planet's surface. If the radius of the planet is , what is the mass of the planet?

**Possible Answers:**

**Correct answer:**

To solve, use Newton's law of universal gravitation:

Remember that the weight of the astronaut is the same as the gravitational force acting between the planet and the astronaut.

We are given the gravitational constant, the radius of the planet, the mass of the astronaut, and the magnitude of the force generated. Using these values in the universal gravitation equation, we can solve for the mass of the planet.

### Example Question #77 : Forces

Suppose that a person on Earth weighs 800N. If this person were to travel to a distant planet that had twice the density and the same radius of Earth, how much will the person weigh on this new planet?

**Possible Answers:**

**Correct answer:**

We are given the weight of a person on Earth in units of Newtons, which means we can recognize this as a force. The force that is acting on this person is the force due to gravity, which can be represented by the following equation:

is the universal gravitational constant and is equal to

is the mass of object 1

is the mass of object 2

is the distance between the centers of the two objects

It's important to note that an object's mass will stay the same no matter where it is, but its weight will vary depending on where it is measured. Notice that when calculating the gravitational force, we need to consider the mass of two objects. If we set the mass of the Earth and the mass of the person in question as the two masses, we can rewrite the equation as:

To calculate how much the person weighs on the new planet, we need to consider the information given - that the new planet is twice as dense as Earth. This means that for a given volume, the new planet will have twice as much mass as Earth. Furthermore, we know that the mass of the person stays the same since, as mentioned above, mass is constant no matter where it is measured. And, if we are considering a case where the volume is the same, then the distance between the centers should also be the same. Thus, we can calculate the new force as:

### Example Question #78 : Forces

How high would you have to be above the Earth’s surface to experience an acceleration of ? (Be careful!)

**Possible Answers:**

**Correct answer:**

This problem can be solved by looking at the formula for the gravitational constant, .

We are looking for the altitude **above** the Earth where the gravitation field is in strength, so we proceed as follows

### Example Question #41 : Universal Gravitation

Two gaseous planets and orbiting a distant star have equal masses, but has 6 times the radius of . What is the relationship between the acceleration of gravity at the surface of these two planets?

**Possible Answers:**

None of these.

**Correct answer:**

Use Newton's law of gravitation to make sense of this problem:

As you can see the force of gravity is inversely proportional to the square of the radius. Since has a radius 6 times larger than , we state that because the acceleration of the gravity of planet two divided by 36 would equal the smaller gravitational acceleration of planet one.

### Example Question #41 : Universal Gravitation

Moon radius:

Moon mass:

Calculate the gravity constant for objects on the surface of the moon.

**Possible Answers:**

**Correct answer:**

Universal Gravitation law:

Assume is the Moon, and is the object on the surface, then:

Will be analogous to in , which will be a negative number since it is pointing down.

Plug in values: