# AP Physics 1 : Specific Forces

## Example Questions

### Example Question #11 : Specific Forces

You are in a small spacecraft that has no windows traveling through space. The craft is accelerating and you have a bathroom scale at your disposal. Before you left Earth that morning you weighed yourself to be . You step on the scale and find it reads . How fast is the craft accelerating in ?

None of these

Explanation:

One thing to note is that the weight measured was given in pounds instead of Newtons. We could convert the weights, but it turns out that we don't need to.

If your weight measured on Earth is

and the weight on the craft is

we know that on Earth the acceleration is . Using Newton's second law,

and

we can set  equal since the mass never changes only the weight force, and solve for ,

This makes sense that you would weigh more if you were experiencing a larger acceleration. This is interesting because you could not tell if you were standing stationary in a gravitational field or accelerating in a non-inertial reference frame. This is what is known as the Equivalence Principle.

### Example Question #12 : Specific Forces

Determine the gravitational constant  on a newly discovered planet, Planet X, if it exerts  of force on a  piece of rock. on the surface.

Explanation:

Using Newton's second law, we can determine the answer.

In our problem,  and .  is the acceleration due to gravity. Therefore,

### Example Question #11 : Forces

A person steps on a scale and reads that his mass is . The person then steps on the scale while on a plane that is inclined at . What is the new mass reading on the scale?

Explanation:

The reading on a scale is really the normal force . On a flat surface, we see the person has a reading of , or . On an inclined surface, one can show that the normal force has a new magnitude of:

### Example Question #11 : Normal Force And Weight

An astronaut of mass  is on a space craft blasting off from the surface of the earth.  after blast off, the acceleration of the ship is . Determine the force the astronaut experiences from her seat at this moment in time.

None of these

Explanation:

Plug in values:

Solve for :

### Example Question #11 : Normal Force And Weight

If the gravitational constant of Mars is , determine the weight of a  object on Mars's surface?

Explanation:

Weight force is given by:

### Example Question #581 : Newtonian Mechanics

A dog is standing on a hill looking for his ball. If the dog's weight is 3 times his normal force, what is the slope of the hill?

Explanation:

We only need the equations for weight and normal force to solve this problem. First the equation for weight (force of gravity):

Now the normal force, which is a function of weight:

If you're unsure why we used cosine, think about the situation practically. As the hill gets flatter (angle decreased), the normal force grows, and cosine is the function that gets larger as the angle gets smaller.

From the problem statement we know that the ratio of weight to normal force is 3:

### Example Question #11 : Forces

Consider the following scenario:

A sledder of mass  is at the stop of a sledding hill at height  with a slope of angle .

The sledder is accelerating down a hill with a slope of  at a rate of . If at time , the sledder has a velocity , how much height does the sledder drop in the next ?

Explanation:

We will start this problem by using the following kinematics equation:

Note that each variable is oriented in the direction of the slope of the hill. We will find the distance traveled along the hill, and then convert that to a height using the slope of the hill.

We already know the value of each variable, so we can find the distance traveled:

Now we can use the slope of the hill and the sine function to determine the height dropped:

We know these values, so let's plug them in:

### Example Question #11 : Forces

A box starts sliding down an adjustable ramp when the angle has reached . Determine the coefficient of friction between the box and the ramp.

None of these

Explanation:

By constructing a force diagram, it can be seen that:

Right when the box starts to move, these will be equal

Solving for

Plugging in values:

### Example Question #12 : Normal Force And Weight

How will the normal force exerted by a chair on an astronaut differ when the rocket is on the launchpad or when it is blasting off?

The normal force will be zero

The normal force will be more during blastoff

None of these

Impossible to determine

The normal force will be less during blastoff

The normal force will be more during blastoff

Explanation:

Concerning the astronaut:

The force of gravity will be essentially constant and downward. Thus, in order for acceleration of the astronaut to increase, the normal force must increase.

### Example Question #11 : Normal Force And Weight

A  box rests on a smooth table. A downward force of  is applied the box. What is the normal force ()?

Explanation:

In this problem the  force acts in the downward direction. The box's weight also acts in the downward direction. We can calculate weight of the box using the equation .

Normal force acts in the opposition to the weight of the box. We can calculate normal force by adding up the downward forces to find the counteracting force on the box.

Forces downward:

Forces upward:

Forces downward are equal to the forces upward. Therefore,