Work is a force times a distance:

We know the distance that the book needs to travel, but we need to sovle for the lifting force required to move it.

There are two forces acting upon the book: the lifting force and gravity. Since the book is moving with a constant velocity, that means the net force will be zero. Mathemetically, that would look like this:

We can expand the right side of the equation using Newton's second law:

Use the given mass and value of gravity to solve for the lifting force.

Now that we have the force and the distance, we can solve for the work to lift the book.

This problem can also be solved using energy. Work is equal to the change in potential energy:

While on the ground, the book has zero potential energy. Once back on the shelf, the energy is equal to . The work is thus also equal to .

The relationship between work, force, and distance is:

We are given the force on the toy and the work done. Using these values, we can find the distance. Note that the mass is not relevant for this question.

The relationship between work, force and distance is:

We are given the value for the force and the distance that the toy travels. Using these values, we can find the work done by the cat. Note that the mass of the toy is not relevant for this calculation.

The relationship between work, force and distance is:

We are given the value for the work done by the cat and the distance that the toy travels. Using these values, we can find the force on the toy. Note that the mass of the toy is not relevant for this calculation.

The formula for work is:

Given the values for force and distance, we can calculate the work done.

Note that no work is done by the force of gravity or the weight of the box, since the vertical position does not change.

Work is the product of force times a distance:

We are given the work and the distance traveled, allowing us to solve for the force. The mass of the cabinet is not necessary information.

Use the data given to calculate the kinetic energy of the rocket at the two different velocities. Then find the amount of work done using the following equation: 

Kinetic energy of the rocket at the two velocities:

The change in the kinetic energy at the two velocities:

Known

Unknown

The work done on the object is equal to the net force done on the object multiplied by the displacement through which the force acts.

Therefore the first thing to do in this problem is to determine the amount of force needed to push the car up the incline.  Since the car is moving at a constant velocity, all forces must be balanced.  The force in the direction of motion is the force applied which is doing work on the object.  The forces opposing motion are the force of friction and the x-component of the gravitational force.

To determine the Force of Gravity in the x-direction, we must break the force of gravity into components and examine the side acting in the x-direction.  Using trigonometric functions we get that 

We know that the force of gravity is equal to mg

The force of friction is directly related to  μ (the coefficient of friction)  times the normal force.  In this case the normal force is equal to the y component of the force of gravity.

Therefore 

We know that our force applied must balance both of these forces.

We can now substitute this equation into our work each to determine the work applied to the car.

We can now substitute in our variables and solve for the missing piece.

Knowns

Unknown

We know that the force of friction is what caused the skid marks and is the cause of the work done on car to slow it to a stop.  We also know that the work is equal to the change in kinetic energy.

Work is equal to the force times the displacement over which the force acted.

Therefore

The force in this case is the force of friction.

Since the car is on a level road the normal force is equal and opposite the force of gravity.

The force of gravity is equal to the mass times the acceleration due to gravity

Therefore 

We can substitute this in for our work-kinetic energy equation.

Since the final velocity is  we can cancel this out of the problem.

Since there is a negative and a mass in both terms we can cancel these out of the equation

Now we can substitute in our values and solve.

The relationship between work, force, and distance is:

We are given the force on the toy and the work done. Using these values, we can find the distance. Note that the mass is not relevant for this question.