# High School Physics : Gravitational Field

## Example Questions

### Example Question #1 : Gravitational Field

What is the acceleration of two falling skydivers (total mass =  including parachute) when the upward force of air resistance is equal to one fourth of their weight?

Explanation:

There are two forces acting on the falling skydivers.  The first is the force of gravity (their weight) which we will denote as .  The second is the force of air resistance pushing up against them which we will denote as .

Newton’s 2nd Law tells us that the net force acting on these two objects is equal to their mass times their acceleration.

The net force is the sum of both forces acting together.

We know that the air resistance acts opposite to gravity and is equal to ¼ their total weight.

Substitute this value into our net force equation.

This simplifies to

The force of gravity is calculated by multiplying the mass by the acceleration due to gravity.

Substitute in our known variables and solve

### Example Question #2 : Gravitational Field

Sally is to walk across a “high wire” that has been strung horizontally between two buildings that are  apart.  The sag (dip) in the rope when she stands at the midpoint is .  If her mass is , what is the tension in the rope at this point?

Explanation:

The first thing is to identify the forces involved in this situation.  There is the force of gravity (or her weight) which is pulling down on the rope.  We can calculate this by

The other forces are the force of Tension on each side of the wire as she stands in the midpoint.  These two Tension forces are what hold up Sally and keep her from falling.  However, these two Tensions forces are at an  angle below the horizontal.  This means that we need to analyze the components of the Tension force.  The -components of each Tension force are equal in magnitude and opposite in direction as this is what keeps the rope connected to both buildings.  The -components of each Tension force are equal in magnitude and in the same direction as they both are keeping Sally up.  So we can sum up the forces acting in the -direction as:

Which can be simplified to

Since Sally is not accelerating, the forces are balanced and the net force must equal .

Earlier we calculated the force of gravity so we can substitute this in to find the Tension in the  Direction.

This is the Tension in the -direction.  However, the problem is asking for the overall Tension in the wire.  At this point, we must use trigonometric functions to determine the hypotenuse (the overall Tension) in the wire.  Since the -component of the Tension is the opposite side of the triangle from the  angle, we can use cosine to find our hypotenuse.

### Example Question #3 : Gravitational Field

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

Explanation:

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 .

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

### Example Question #4 : Gravitational Field

ball falls off a cliff. What is the force of gravity on the ball?  Assume

We need to know the height of the cliff in order to solve

We need to know the time the ball is in the air in order to solve

Explanation:

Newton's second law states:

In this case the acceleration will be the constant acceleration due to gravity on Earth.

Use the acceleration of gravity and the mass of the ball to solve for the force on the ball.

The answer is negative because the force is directed downward. Since gravity is always acting downward, a force due to gravity will always be negative.

### Example Question #5 : Gravitational Field

A woman stands on the edge of a cliff and drops two rocks, one of mass  and one of , from the same height. Which one experiences the greater acceleration?

The rock with mass

They experience the same acceleration

The rock with mass

We need to know the height of the cliff in order to solve

We need to know the density of the rocks in order to solve

They experience the same acceleration

Explanation:

Even though the rocks have different masses, the acceleration on both will be , the acceleration due to gravity. We can look at Newton's second law to see the force experienced by the rocks:

When objects are in free-fall, the acceleration will be equal to the acceleration from gravity, regardless of the mass of the object.

### Example Question #6 : Gravitational Field

A person stands on a scale in an elevator.  His apparent weight will be the greatest when the elevator

Standing still

Is accelerating downward

Is moving upward at constant velocity

Is accelerating upward

Is moving downward at constant velocity

Is accelerating upward

Explanation:

Consider a person standing on a scale in an elevator that is not moving.  The person is exerting a downward force onto the scale equal to their weight force.  The scale exerts a force upward that is equal to the downward force of gravity.  This upward force is the reading on the scale.

Now consider a person standing on a scale in an elevator that is moving at a constant velocity.  The person is exerting a downward force onto the scale equal to the force of gravity.  The scale exerts a force upward.  Because the elevator is moving at a constant velocity, these forces are balanced, and the scale would read the same as if you were not moving.

Now consider a person standing in an elevator that is accelerating.  There are still two forces, the downward force of gravity, and the upward normal force.  Since the elevator is accelerating, these forces are unbalanced in the direction of the motion.  If the elevator is accelerating down, gravity is larger than the normal force.  If the elevator is accelerating up, the normal force is greater than gravity.

Since the scale reads the magnitude of the normal force, the time when the normal force is the greatest is when the elevator is accelerating in an upward direction.

### Example Question #7 : Gravitational Field

weight and a  weight are dropped simultaneously from the same height.  Ignore air resistance.  Compare their accelerations.

The  weight accelerates faster because it is heavier

The  weight accelerates faster because it has a smaller mass

They both accelerate at the same rate because they have the same weight to mass ratio.

The  weight accelerates faster because it has more inertia

They both accelerate at the same rate because they have the same weight to mass ratio.

Explanation:

### Example Question #8 : Gravitational Field

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

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 #9 : Gravitational Field

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 #10 : Gravitational Field

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 will increase, but her mass will decrease

Her weight will remain the same and her mass will decrease

Her weight will decrease and her mass will remain the same

Her weight and mass will decrease

Her weight and mass will remain the same

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.