Work is a force times a distance or . 

Only one of these has a force times a distance: the weightlifter lifting a weight above his head.

The car moving at a constant velocity has no acceleration and therefore no force.

Typing essays does not require a force times a distance (though it sure feels like work!).

If the skier has no loss in energy, then no work was done, as work is also the measurement of the change in energy.

The man sitting in a chair has a constant velocity of zero, no acceleration, and therefore no force.

Known

Unknown

We can use the work kinetic energy theorem to solve this problem.  The work done to the object causes a change in kinetic energy.

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

Therefore

Plug in our variables and solve

Work is a force times a distance:

We know the distance that the book needs to travel, but we need to solve 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. Mathematically, 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 .

Work is the product of a net force over a given distance.

In order for there to be work, there must be a net force applied and the object must have a non-zero displacement. In this question we are given the displacement, but we have to solve for the force.

The question only tells us that the couch moves with constant velocity. This tells us that acceleration is zero. If acceleration is zero, then force must also be zero according to Newton's second law.

If the force is zero, then the work is also zero.

Known

Unknown

When something does work on an object it changes the total energy of the object.  In this case, the work done by the person converts to kinetic energy as the stone is launched.  This kinetic energy is then turned into gravitational potential energy when the stone is at the highest point of the peak.

Work done = Kinetic Energy when the stone leaves the hand = Gravitational Potential Energy at the peak

We can set the work done to the gravitational potential energy

Plug in our known values and solve.

Known

We need to convert our velocity to 

Unkonwn

The easiest way to solve this problem is through conservation of energy.  When the car is rolling along the road it has kinetic energy.  Once the spring brings it to a complete stop, the car has elastic potential energy. According to the law of conservation of energy, these two values should be equal to one another

We can now plug in our known values and solve for the missing variable

The equation for potential energy is . We are given the mass of the ball, the height of the table, and the acceleration of gravity in the question. The distance the ball travels is in the downward direction, making it negative.

Plug in the values, and solve for the potential energy.

The units for energy are Joules.

Knowns

Unknowns

Equation

Plug in the vales and solve for the stretch of the spring.

Work causes a change in the kinetic energy of an object.  In the example of a car stopping, the work done on the car causes the car to slow down to a stop, therefore changing the kinetic energy.

Work is also equal to the force times the displacement of the object. In this case, we are assuming that the force applied to stop the car does not change.

Since the car is coming to a stop the final velocity of the car is 0m/s.

Therefore when you double the velocity, that value is then squared.

Therefore your kinetic energy is increased by  times the original amount.

If your kinetic energy is  times greater, than with the same force being applied, the stopping distance will also increase by  times since they are directly related.

Hooke’s law states that spring constant is directly related to the force applied and the distance that the object is stretched.

We also know that the potential energy of a spring is related to the spring constant and the distance that the object is stretched

We can substitute our equation for Hooke’s law into the potential energy equation.

This simplifies to

This equation shows that there is a direct relationship between the force on the spring and the potential energy of the spring.  If the force is doubled, then the potential energy will likewise double.