# High School Physics : Understanding Gravity and Weight

## Example Questions

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### Example Question #1 : Understanding Gravity And Weight

Michael lands on a new planet. If his mass is  and the acceleration due to gravity on this planet is , what would his weight be?

Explanation:

Weight is a particular force that is equal to mass times acceleration due to gravity. Start with Newton's second law, .

Plug in the given values to solve.

### Example Question #2 : Understanding Gravity And Weight

Leslie is an astronaut on a new planet. She knows her mass is , and she can calculate her weight on the planet to be . What is the acceleration due to gravity on the new planet?

Explanation:

Weight is a specific force. It is always equal to the mass times acceleration due to gravity:.

Plug in the given values to solve for the acceleration.

The gravitational acceleration is negative because it acts in the downward direction.

### Example Question #3 : Understanding Gravity And Weight

Jenny calculates that her weight on Earth is equal to . Assuming acceleration due to gravity on earth is equal to , what is her mass?

Explanation:

Weight is a specific force that is always equal to mass times acceleration due to gravity.

Plug in the given values to solve for the mass.

### Example Question #1 : Understanding Gravity And Weight

Jerry wants to lift a  ball with exactly enough force so that it's upward velocity is constant. How much force should he use?

Explanation:

If the velocity on an object is constant, that means it has no acceleration. If it has no acceleration, that means that the net force on the object is equal to zero. We can see this conclusion by using Newton's second law.

Another way to think of  is the sum of all the forces. Since the only two forces acting upon the ball are gravity and Jerry's lifting force, we can see: .

Since the net force is zero, the magnitude of Jerry's force must equal the magnitude of the force of gravity, but in the opposite direction.

This means that once we find , then Jerry's lifting force will be the same magnitude but in the opposite direction. Use Newton's second law to find the force of gravity.

This means that Jerry's lifting force will be .

### Example Question #5 : Understanding Gravity And Weight

The acceleration of gravity on the moon is significantly less than the acceleration of gravity on earth. What will happen to an astronaut's weight and mass on the moon, compared to her weight and mass on Earth?

Her weight and mass will remain the same

Her weight will remain the same and her mass will decrease

Her weight will increase, but her mass will decrease

Her weight will decrease and her mass will remain the same

Her weight and mass will decrease

Her weight will decrease and her mass will remain the same

Explanation:

Mass is a measure of how much matter is in an object, while weight is a measurement of the effective force of gravity on the object.

The amount of matter in the astronaut does not change; therefore, she has the same mass on the moon as she has on Earth.

Her weight, however, will change due to the change in gravity. The force of gravity will be the product of the acceleration and the astronaut's mass.

If the gravity is less on the moon than on Earth, then the force of gravity on the astronaut will also be less on the moon; thus, she will weigh less.

### Example Question #6 : Understanding Gravity And Weight

If the mass of the object is  and , what is the value of W?

Explanation:

W will be the weight of the object. Weight is a very specific force: it is the mass times gravity. As it turns out, the angle is irrelevant in finding weight.

Using Newton's second law and the given values for mass and gravity, we can solve for W.

Note that the weight is negative, because it is acting in the downward direction.

### Example Question #2 : Understanding Gravity And Weight

An astronaut lands on a new planet and discovers her weight on this planet is half of her weight on Earth. What is the acceleration due to gravity on this planet in terms of the acceleration due to gravity on Earth ()?

We need to know her mass in order to solve

Explanation:

Weight is a very specific force, equal to the mass times gravity:

On this new planet her weight is half of what it was on Earth. We can write this mathematically, using the weight equation.

Mass cancels out from each side, leaving a relationship between the gravitational accelerations.

That means the acceleration due to gravity on this new planet is half of what it was on earth.

### Example Question #8 : Understanding Gravity And Weight

A ball that weighs  on Earth weighs on a recently discovered planet. What is the force of gravity on this new planet?

Explanation:

Weight is defined as the force of gravity on an object. We can use Newton's second law to write an equation for weight.

If the ball weighs  on Earth, then its mass can be found using this equation and the acceleration of gravity on Earth.

Use this mass and the given weight on the new planet to find the acceleration of gravity on this new planet. Though our initial values (and thus our final values) only allow one significant figure, we will not round until the end of all calculations. This ensures that we preserve accuracy before adjusting for precision.

Adjust this value to one significant figure by rounding up. The zero in the tens place is before the decimal, and is not considered significant.

### Example Question #1 : Understanding Gravity And Weight

An object is placed in the direct center of the Earth. What would be the perceived weight of the object?

The object would have infinite weight upward

The weight of the object would be equal to its weight at the Earth's surface

The object would have no weight

The object would have infinite weight downward

We must know the mass of the object to draw a conclusion

The object would have no weight

Explanation:

We must use Newton's law of universal gravitation to solve this question.

There are three variables that really change the force of gravity: the mass of each object and the distance between the bodies.

The important thing to recognize here, though, is that when an object is in the center of the earth, the mass of the earth is distributed symmetrically all around it. It's like being in the center of a giant bubble. Because the mass is symmetrically distributed, the mass that is trying to pull the object in each direction is equal. Essentially, the mass pulling upward cancels out the mass pulling downward, and the mass pulling right cancels out the mass pulling left.

This happens for the entirety of the circle, leaving you with a net force of zero acting upon the object.

### Example Question #10 : Understanding Gravity And Weight

A satellite is in orbit  above the Earth. What is the relationship between the acceleration due to gravity on the satellite, versus the acceleration due to gravity on the Earth's surface?

Acceleration due to gravity on the satellite will be greater than

Acceleration due to gravity on the satellite will be less than

Acceleration due to gravity on the satellite will be equal to

Acceleration due to gravity on the satellite will be

We would need to know the mass of the satellite to solve

Acceleration due to gravity on the satellite will be less than

Explanation:

For this problem, we are comparing the force of gravity on the surface, or weight, to the force of gravity on the satellite. We can use Newton's second law to find the weight of the satellite, and the law of universal gravitation to find the gravity on the satellite. These two terms will be equal to one another.

Let's call  the Earth and  the mass of the satellite.

Notice that the masses of the satellite cancel out.

This formula gives us the acceleration of gravity in terms of the mass of the Earth and the distance from the Earth's center. We can write two separate equations, one for the surface and one for the satellite. Since the mass of the Earth doesn't change and  is a constant, the only variable that can change is , the distance between the objects.

On Earth,  is the radius of the earth. For the satellite,  is the radius of the Earth PLUS the orbiting distance; therefore . Because we are dividing by our , a greater  gives us a smaller .

The satellite in space will have a smaller acceleration due to gravity. It will not be zero, but it will be smaller than the acceleration on the surface.

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