# AP Physics 1 : Newton's Second Law

## Example Questions

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### Example Question #1 : Newton's Second Law

A man of mass 50kg on the top floor of a skyscraper steps into an elevator. What is the man's weight as the elevator accelerates downward at a rate of ?

Explanation:

Use Newton's second law to solve this problem.

When the elevator is not moving, we get

However, when the elevator is accelerating downward, the man appears to be lighter since the elevator is negating some of the force from gravity. Written as an equation, we have:

Where  is acceleration due to gravity and  is the acceleration of the elevator.

Putting in our values, we get:

### Example Question #2 : Newton's Second Law

A skydiver of mass 70kg has jumped out of a plane two miles above the surface of the earth. After 20 seconds, he has reached terminal velocity, meaning he is no longer accelerating. What is the force of the air on the skydiver's body?

Explanation:

This question is testing your understanding of terminal velocity and Newton's second law. Since the skydiver is at terminal velocity, the force of the air is equal to the force of gravity, resulting in zero net force and thus no acceleration. We just need to calculate the force of gravity on the skydiver to find the force of the air:

### Example Question #3 : Newton's Second Law

A skydiver of mass  is mid jump and has an instantaneous acceleration of . What is the force exerted on the diver from the air?

Explanation:

There are two forces in play in this scenario. The first is gravity, and the second is air resistance. Since they are opposing each other, we can write:

Substituting in Newton's second law, we get:

Rearranging for the force of air resistance, we get:

Plugging in our values from the problem statement:

### Example Question #1 : Newton's Second Law

A diver of 50kg jumps from a platform 20m high into a pool. If the diver decelerates at a constant rate to zero velocity in 0.8 seconds after hitting the water, what is the force that the water exerts on the diver?

Explanation:

We can use the equation for conservation of energy to calculate the velocity of the diver as he hits the water:

Cancel out initial kinetic and final potential energies, and plug in our expressions:

Cancel out mass and rearranging for final velocity:

Plug in our values:

We know that the diver then decelerates from this velocity to zero in 0.8 seconds, so we can calculate the acceleration:

Then use Newton's second law to calculate the force on the diver:

### Example Question #1 : Newton's Second Law

A 2000kg car with a velocity of  collides head on with a 6000kg truck with a velocity of . Which vehicle experiences the greater force? Which experiences the greater acceleration?

The truck experiences the greater force and the greater acceleration

The car and the truck experience equal force and the car experiences greater acceleration

The car experiences the greater force and the greater acceleration

The truck experiences the greater force and the car experiences the greater acceleration

Both the car and the truck experience equal force and acceleration

The car and the truck experience equal force and the car experiences greater acceleration

Explanation:

The car and the truck experience equal and opposite forces, but since the car has a smaller mass it will experience greater acceleration than the truck according to the equation F = ma.

A greater mass will decrease the acceleration.

### Example Question #6 : Newton's Second Law

A man is rolling a recycling bin of mass  down his driveway, which has a slope of , at a constant velocity when he accidentally drops it. What is the total frictional force on the recycling bin if it is decelerating at a rate of ?

Explanation:

Since we are neglecting air resistance, there are two forces in play: gravity and friction. Therefore, we can use Newton's second law to write the following:

Substituting in an expression for the force of gravity and rearranging for the force of friction, we get:

### Example Question #1 : Newton's Second Law

If we apply a constant force of  on a  object that is located on a frictionless surface, what is the acceleration of the object?

Explanation:

Use Newton's second law.

### Example Question #8 : Newton's Second Law

A constant force of 30N acts on a a 10kg box as shown in the diagram. If the box is originally at rest, what will be its velocity after 5s?

Explanation:

The box has a constant force acting on it pulling it towards the left. Therefore we can write this as:

, where the negative sign indicates that the force is directed towards the left.

Since the force is constant, this means that is is causing the box to move with a constant acceleration that we can calculate using Newton's second law of motion:

Now that we know the acceleration, we can calculate the final velocity after 5 seconds:

Where  and  since the box is originally at rest.

So we have that

.

Note that the negative sign indicates that the box is moving to the left.

### Example Question #1 : Newton's Second Law

A 10kg box is being pushed across a frictionless field by two people. The box is moving with an acceleration of  . What is the force applied by the weaker person if the stronger person can push twice as hard?

Explanation:

The force applied by the weaker person can be calculated using Newton's second law, which states:

The net force is equal to the product of the mass of the object and the acceleration of the object. We were given the mass and acceleration of the object, but only the ratio of the applied forces:

Solve for , the applied force from the weaker person:

### Example Question #1 : Newton's Second Law

Is it possible to have a non-zero number of forces acting on an object (of non-zero mass), yet the object doesn't acclerate?

Yes

No