### All AP Physics 1 Resources

## Example Questions

### Example Question #1 : Other Forces

A scuba diver and his equipment have a total mass of and a total volume of . If he wants to maintain a constant depth of , what average vertical force must he exert on the water with his flippers?

**Possible Answers:**

None of the other answers

**Correct answer:**

If the diver stays at a constant depth, we know that all the forces on him must cancel out:

We can write out all of the forces on the diver, using force of the flippers to denote the vertical force he exerts to stay at constant depth:

The force of gravity and bouyancy counteract each other, so they will have opposite signs. If we assume that the force of flippers will be down, we can write:

The bouyancy force is simply the weight of the water displaced by the diver. Plugging in expressions for the latter two forces:

We have values for all of these, allowing us to solve:

### Example Question #1 : Other Forces

A spring is attached to the top of a box. The constant of the spring is and a block of mass attached to the other end. If the spring is initially compressed past equilibrium, at what rate is the box initially accelerating? Is the initial acceleration up or down?

**Possible Answers:**

**Correct answer:**

Since the spring is initially in equilibrium, we can write:

There are three forces in play: spring force, gravitational force, and the additional force resulting from the acceleration of the box. If we say that any forces pointing downward are positive, we can write:

The force resulting from the additional acceleration must be subtracted since all forces cancel out and both of the other two forces are postive. This means that the resulting force from acceleration is pointing upward; Thus, the box is accelerating downward (think about riding in an elevator).

Substituting expressions for each force, we get:

Rearrange to solve for the acceleration of the box:

### Example Question #2 : Other Forces

Consider the following scenario:

If the force of tension is , the coefficient of static friction is , and the angle measures , what is the maximum mass of the block that will result in motionlessness?

**Possible Answers:**

**Correct answer:**

There are three relevant forces in play in this scenario: friction, tension, and gravity.

We can use Newton's second law to create an expression for the net force:

Substituting expressions in for the forces, we get:

Rearrange to solve for the mass:

Use our given values to solve:

### Example Question #3 : Other Forces

An astronaut is in orbit around the earth. The feeling of weightlessness that he experiences is due to the absence of which force?

**Possible Answers:**

Gravitational force

Normal force

Frictional force

Buoyant force

**Correct answer:**

Normal force

The correct answer is normal force. Normal force will occur when the astronaut is standing on a surface, which will push back on him. Gravity is present since the astronaut is in orbit (gravity provides the centripetal force). The feeling of weightlessness he experiences is due to the absence of a surface to push back on him/her.

### Example Question #5 : Other Forces

Consider a sphere with a radius. What weight would a scale read if the sphere was halfway submerged in water? Take the density of water to be^{}(A picture will help).

**Possible Answers:**

**Correct answer:**

To solve this problem, we need to look at all of the forces acting on the sphere, this includes the force of gravity, the normal force provided by the scale, and the buoyancy force. If the object is in equilibrium, the net force acting on the sphere must be zero.

### Example Question #6 : Other Forces

Suppose that a student pushes his physics textbook across the table with his hand. In doing so, what type of force is acting on the book?

**Possible Answers:**

Weak force

Strong force

Electromagnetic force

Gravitational force

**Correct answer:**

Electromagnetic force

If a person were to use their hand to push a book across the table, the type of force that their hand is applying to the book is classified as an electromagnetic force. Even though this may not seem intuitive, the reason is that the electrostatic repulsion of the atoms in the person's hand repel the atoms in the book. Due to this electrostatic repulsion between the atoms in the person's hand and the atoms in the book, the force is electromagnetic.

Gravitational forces occur due to gravity, that is, from an attraction between any two objects with mass. The strong and weak forces are both nuclear forces that act only across very, very short distances. Generally, these forces are only significant at the sub-atomic level in the atom's nucleus, and thus do not have a role at greater distances (such as between the person's hand and the book).

### Example Question #7 : Other Forces

Mass of Mars:

Universal gravitation constant:

Radius of Mars:

A buggy on the surface of Mars locks up it's break and slides on Martian ice. If the buggy was traveling at and took to stop. Determine the coefficient of friction between Martian ice and the tires.

**Possible Answers:**

None of these

**Correct answer:**

The normal force will be equal to the magnitude of the force of gravity pushing the buggy into the ground.

Using definition of frictional force and work equation:

Combining equations:

Canceling out the mass of the buggy and plugging in values:

Solving for

### Example Question #8 : Other Forces

An adventurous teenager has decided to pick up skydiving. If the teen has a mass of , a reference area of , and a terminal velocity of , what is the density of the air through which the diver is traveling?

**Possible Answers:**

**Correct answer:**

When a diver reaches terminal velocity, we know that the net force on the diver is equal to 0. There are two forces acting on the diver, gravity and drag, so we can say that:

Plugging in expressions, we get:

Rearranging for density, we get:

We have all of these values, so we can plug and chug:

### Example Question #4 : Other Forces

A car travels around a circular racetrack at a velocity of . The radial distance between the center of the racetrack and the center of the car at any given point of its trip is . What is the centripetal force on the car?

**Possible Answers:**

**Correct answer:**

This question tests your understanding of the concept of centripetal force. Centripetal force is a force that maintains a body's circular travel along a curved surface and points inward towards the center of the curve from each point that the body travels along. Centripetal force is calculated as follows:

Therefore the centripetal force on the car is .

### Example Question #5 : Other Forces

Nicola is attempting to create a single tiered mobile as shown. She has a wooden dowel (, ), and two distinct bird ornaments (, ) which she wishes to attach on either end of the dowel.

If Nicola places ornament , to the left of the dowel's midpoint, and ornament , to the right of the dowel's midpoint, where should she attach the mobile string in order for it to balance?

Note: figure not drawn to scale.

**Possible Answers:**

from the right end of the dowel

from the left end of the dowel

from the left end of the dowel

from the right end of the dowel

**Correct answer:**

from the left end of the dowel

Let's use the midpoint as our point of reference. With that said, is from the center, and is from the center. However, each of these are on *different sides of the midpoint.* When we set up our center of gravity equation, we must determine a (+) and (-) side in order to denote under which side our mobile string will fall. It may be helpful to look at the mobile as a number line, with the left being negative, and the right side positive, but you can really use which ever is more comfortable.

Our main equation is this:

Where is our weight in newtons and is our distance in meters. Typically, we would want to convert everything to SI units, so let's go ahead and do that (ex: )

Now let's plug in our numbers, remember about our negative/positive sides!

This should give us

Now, because this number is negative, we know it's to the *left* of our midpoint (if you chose to set up your -/+ sides opposite of how we did it, your answer will be positive). Regardless of the outcome, this measurement is meant to be taken from object *A* to the midpoint. Well, do any of our answers have either (+) or (-) ? No. But if we read them carefully, we can determine that the answer is from the left of the dowel by using simple subtraction.

One side is

Think about it logically too (use your pencil). The heavier end of a pencil usually has a bulky eraser on it (just like the bulkier object on the left). Try holding the pencil at the tip's end, and then gradually try balancing it in the same manner as you move closer to the eraser.

ALSO NOTE: the question states the weight of the dowel as well. But look we didn't even need it. Sometimes the AP exam will give you some aspects in the question to distract you.

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