AP Physics 1 : Newtonian Mechanics

Study concepts, example questions & explanations for AP Physics 1

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Example Questions

Example Question #1 : Torque

One side of a seesaw carries a  mass four meters from the fulcrum and a  mass two meters from the fulcrum. To balance the seesaw, what mass should be placed nine meters from the fulcrum on the side opposite the first two masses?

Possible Answers:

Correct answer:

Explanation:

For the seesaw to be balanced, the system must be in rotational equilibrium. For this to occur, the torque the same on both sides.

The total torque must be equal on both sides in order for the net torque to be zero.

Substitute the formula for torque into this equation.

Now we can use the given values to solve for the missing mass.

The acceleration form gravity cancels from each term.

Example Question #1 : Torque

Two masses hang below a massless meter stick. Mass 1 is located at the 10cm mark with a weight of 15kg, while mass 2 is located at the 60cm mark with a weight of 30kg. At what point in between the two masses must the string be attached in order to balance the system?

Possible Answers:

Correct answer:

Explanation:

This problem deals with torque and equilibrium. Noting that the string is between the two masses we can use the torque equation of . We can use the equation to find the torque. Since force is perpendicular to the distance we can use the equation  (sine of 90o is 1). Force presented in this situation is gravity, therefore F=mg, and using the variable x as a placement for the string we can find r.

x=43, thus the string is placed at the 43cm mark.

Problem2

Example Question #1 : Torque

An attraction at a science museum helps teach students about the power of torque. There is a long metal beam that has one pivot point. At one end of the bar hangs a full sedan, and on the other end is a rope at which students can pull down, raising the car off the ground.

The beam is 40 meters long and the pivot point is 5 meters from one end. A car of mass 500kg hangs from the short end of the beam. Neglecting the mass of the beam, what is the minimum mass of a student who can hang from the rope and begin to raise the car off the ground?

Possible Answers:

More information is needed to answer

Correct answer:

Explanation:

We are trying to find what force needs to be applied to the rope to result in a net of zero torque on the beam.

Torque applied by the car:

We can use this to find the mass of a student that will create the same amount of torque while hanging from the rope:

Example Question #1 : Torque

There is a  weight  to the left the center of a seesaw. What distance from the center on the right side of the seesaw should Bob sit so that the seesaw is balanced?

Bob's mass is 

Possible Answers:

Correct answer:

Explanation:

Torque is defined as . In this case, is zero because Bob and the weight are sitting directly on top of the seesaw; all of their weight is projected directly downward. Therefore, the torque that the weight applies is:

In order for the seesaw to balance, the torque applied by Bob must be equal to .

Example Question #11 : Torque

Terry is pushing a vertical lever that is attached to the floor, and he pushes  above the point of rotation. If he pushes with a force of  at an angle of  from the ground, what is the magnitude of torque that he is applying to the lever's hinge?

Possible Answers:

Correct answer:

Explanation:

Magnitude of torque can be found by relating the amount of force applied perpendicular to a lever arm about a point of rotation.

In this case, the force is not perpendicular, so we must take the perpendicular aspect of the force to find torque.

Plug in and solve.

Example Question #11 : Torque

From the given force and position vector, calculate the torque experienced by an object.

Possible Answers:

Correct answer:

Explanation:

To calculate the torque experienced by the object, we must take the cross product of the force vector and the position vector.

Example Question #11 : Torque

You apply a force of  to a wrench of length . Determine the torque experienced by the bolt on the other end. Assume the force you apply is perpendicular to the wrench.

Possible Answers:

None of these

Correct answer:

Explanation:

The definition of torque is

 Where

 is the force

 is the distance

Theta is the angle between the direction of the force and the distance.

 

In this case, , so  .

 

Plugging in our remaining values:

 

 

Example Question #1051 : Newtonian Mechanics

There is a steel disk of radius and uniformly distributed mass . Assuming that it is perfectly balanced on it's center, determine how much torque would be needed to accelerate it to  in .

Assume

Possible Answers:

Correct answer:

Explanation:

Initial angular momentum is zero

Combine equations:

Solve for

Definition of :

Combine equations:

Plug in values:

Example Question #11 : Torque

A force  is applied to the edge opposite the doorhinge of a door of radius  perpendicular to the door to produce a torque . Suppose now that the force is doubled, but now acts at a point  from the doorhinge at an angle of  to the door. 

What is the resulting torque in terms of ?

Possible Answers:

Correct answer:

Explanation:

The torque  is produced by a force  acting at a radius . Since the force and the radius are perpendicular, then the torque equation gives us:

 

The new torque, which we will call  is produced by a force of  acting at a radius of  at an angle of . Thus the torque equation gives us:

Since , plugging this in to the above gives us 

Example Question #1055 : Newtonian Mechanics

Find the torque  on a rod that's  in length that's hit by a  force at a  angle.

Possible Answers:

Correct answer:

Explanation:

Torque is given by:

, where  is the length of the rod from the pivot point,  is the force acting on the rod, and  is the angle. Since we have all of these components, we can plug in and solve:

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