AP Physics 1 : Newtonian Mechanics

Study concepts, example questions & explanations for AP Physics 1

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Example Questions

Example Question #21 : Work, Energy, And Power

Object A does work on Object B. The sum of change in potential energy and change in kinetic energy is __________ for object A and __________ for object B.

Possible Answers:

negative . . . negative

positive . . . negative

positive . . . positive

negative . . . positive

Correct answer:

positive . . . negative

Explanation:

Recall that work can be defined as the change in energy of a system. For most systems, we deal with two types of energy: potential and kinetic energy; therefore, work is defined as follows.

Where  is work,  is change in kinetic energy, and  is change in potential energy. Work can be negative or positive based on the type of work being performed. If work is done by an on object (such as object A) then it will have a positive value for work. However, if work is being done on the object (such as object B) then the object will have a negative value for work. We already defined work as being the sum of change in potential energy and change in kinetic energy; therefore, this sum will be positive for object A (positive work) and negative for object B (negative work). Note that both object A and object B will have the same, absolute value for work.

Example Question #21 : Work, Energy, And Power

During takeoff, a rocket goes from at of elevation to at of elevation.

 Estimate the amount of work done by the rocket engine. Neglect any mass change due to burning of fuel.

Possible Answers:

Correct answer:

Explanation:

Initially there is only potential energy, and in the final state there is both kinetic and potential.

Plug in all values and solve:

Example Question #23 : Work, Energy, And Power

Determine the work done by pushing a 1kg object up a  incline that is  long. Assume no friction or air resistance is acting. .

Possible Answers:

Correct answer:

Explanation:

Since the only force acting is gravity, we can determine work by determining the potential energy change. 

Since potential energy is given by:

, where  is mass,  is the gravitational constant, and  is height above the earth, we can determine work done by determining:

We can assume 

To determine , we determine the height above the ground that the object is moved. We do this by doing:

Therefore,

Example Question #21 : Work, Energy, And Power

Consider the following system:

 

Spinning rod with masses at end

Two spherical masses, A and B, are attached to the end of a rigid rod with length l. The rod is attached to a fixed point, p, which is at the midpoint between the masses and is at a height, h, above the ground. The rod spins around the fixed point in a vertical circle that is traced in grey.  is the angle at which the rod makes with the horizontal at any given time ( in the figure).

The rod is initially at rest in its horizontal position. How much work would it take to rotate the rod clockwise until it is vertical, at rest, and mass A is at the top?

Neglect air resistance and internal frictional forces. Ignore the mass of the rod itself.

Possible Answers:

None of these

Correct answer:

Explanation:

We can use the expression for conservation of energy:

Since the rod is both initially and finally at rest, we can removed both kinetic energies. Also, if we assume point p is at a height of 0, we can removed initial potential energy, leaving us with:

Plugging in the expression for potential energy and expanding for both masses:

Since the rod is vertical, we know that mass A is half a rod's length above our reference height, and mass B is half a rod's length below it. Thus we get:

Factoring to clean up our expression:

We know all of our variables, so time to plug and chug:

Example Question #22 : Work, Energy, And Power

A box is being pushed along a frictionless surface by a  force, , directed at an angle of  below the horizontal.  If the block covers a horizontal distance of , how much work, , was done on the box?

Possible Answers:

Correct answer:

Explanation:

The box is moving horizontally across the surface, which means that only the horizontal component of the applied force will do work on the box.  The horizontal component of the force is given by 

.  Therefore, to calculate the work done by the applied force, we will use the standard definition of work, given as

Example Question #24 : Work, Energy, And Power

 box slides  down a  inclined plane.  If , calculate the magnitude of the work done by friction on the box, .  Your answer should only have  significant figures.

Possible Answers:

Correct answer:

Explanation:

In general,

In order to calculate the work done by a force, we need to find the angle between the force and the displacement through which the object moves.  Since the displacement is directed down the incline, then this means the friction force acts up the incline.  This means .  We must remember the frictional force is represented as

Where  is the normal force and  is the coefficient of kinetic friction.  On an inclined plane, we can show that .  Therefore, we can finally write 

 

Plugging in everything, and noting the magnitude is the absolute value of a quantity, we can plug in for our answer:

Example Question #25 : Work, Energy, And Power

 block slides up an incline at a initial speed .  The block slides a distance of  until coming to a stop.  Calculate the work done by the normal force, .

Possible Answers:

Correct answer:

Explanation:

Because the normal force  is always perpendicular to the displacement , the normal force does no work on the block, so 

This can also be shown mathematically by plugging in zero for theta in the equation for normal force:

Example Question #23 : Work, Energy, And Power

 ball is initially compressed against a spring  on a frictionless horizontal table.  The ball is the released, and is shot to the right by the spring.  Calculate the work done by the spring on the ball, .

Possible Answers:

Can not be determined.

Correct answer:

Explanation:

From the Work-energy theorem,

.  

From conservation of energy, we see that all of the potential energy contained in the spring will be transferred into kinetic energy of the ball, shown as 

 

Noting the initial kinetic energy of the ball is , we can see that the work done by the spring will be equal to the initial potential energy of the spring.

Example Question #21 : Work, Energy, And Power

An 500kg elevator is at rest. If it is raised 50 meters and returns to rest, how much total work was done on the elevator?

Possible Answers:

Correct answer:

Explanation:

This can be a tricky question. You need to rely on the work-energy theorem, which states:

Since the elevator is at rest at both the beginning and end, the net work is 0; there is no net change in energy, and therefore no work.

This theorem can be confusing to some since it completely negates potential energy. However, let's think about the situation presented in the problem. A force is required to raise the elevator, meaning that energy is put into the system. However, since it comes back to rest, all of the energy that was put in has been removed by the force of gravity, resulting in a net of zero work.

Example Question #26 : Work, Energy, And Power

A rocket of mass is motionless at the origin. The rocket then fires. At location , it is traveling at .

Determine the work done on the rocket

Possible Answers:

None of these

Correct answer:

Explanation:

Determining magnitude of final velocity:

Plugging in values:

Using definition of kinetic energy:

Plugging in values:

Since there was no initial kinetic energy:

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