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Problem #1

A 45.0 kg box is moved with constant speed from A to B along the two paths shown. Calculate the work done by gravity on each of these paths.

This leads to the definition of conservative force

Part b

The same box is pushed across a floor from A to B along the paths shown. If the coefficient of friction betwen the box and the floor is 0.63, how much work is done by friction along each path?

As expected the conservative force of gravity gives the same work, regardless of path.

The work done by kinetic friction is nonconservative and is therefore path dependent. This is shown by the differing values of work even though the box ends up in the same location.

A conservative force is a force that does zero total work on any closed path.

Closed Paths

A good example of this is a rollercoaster

When the rollercoaster car returns to its original position, the total kinetic energy is zero and therefore the total work done by gravity is zero.

Similar to the International Space Station returning to its original position, if work is done on a closed path its total work is zero.

Conservative Vs. Nonconservative Forces

In physics, we classify forces as conservative or nonconservative.

Conservative Forces

Nonconservative forces

Example

The simplest case of a conservative force is gravity.

Conservative forces are forces that do work that is stored in the form of energy that can be released at a later time.

In nonconservative forces the energy cannot be accessed at a later date. This is usually the result of energy lost in another form.

When you lift a box the work done is mgh.

When you let go of the box, the work done by gravity is mgh.

This is conservative because the work energy you put into the box is stored to be used by gravity.

The simplest example is kinetic friction.

When you slide a box of mass m across the floor, you must exert a force of magnitude µmg.

When you stop pushing the box it stays put because the energy input is not conserved.

The work energy has been "lost" to other forms of energy, such as heat. (Think Mr. Myogi.)

Conservative and Nonconservative Forces

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