Work 

 

 The concepts of work and energy are closely tied to the concept of force because an applied force can do work on an object and cause a change in energy. Energy is defined as the ability to do work.

Seems like a bit of circular logic, but think of it this way.  You can apply a force on an object to change the property of that object.  Simply put imagine pushing a stationary bowling ball, now a couple of things might happen. If the ball is on a smooth flat track the ball will start rolling then start going faster and faster.  Next if the bowling is pushed up a steep incline, so steep that the ball never really picks up speed, as a matter of fact, when you reach the top of the hill and you stop pushing, the ball stops.  Lastly If the ball is on a rough track, so rough the ball wont move.  

1.  In the first case the work done on the ball speeds it up, increasing it motivational energy (call kinetic energy) 

2.  Work is still done in the second case even if the balls speed doesn't change.  At the top of the hill the ball has the potential to go faster, potential energy.  If the ball slides down the hill, it will go faster and faster. 

3.  In the third case, the energy of the bowling ball doesn't change, it's motion doesn't change nor does its height.

 When talking about negative and positive work it is important to consider what work is and why we calculate work.  There are two ways of looking like work.

The first way is work is done when one form of energy is transformed into another, now we haven't talked about energy but understand that there is two types of mechanical stored and motional based.  To transform motion energy to stored energy work has to be done, or vise verse, even transforming one form of stored energy to another work has to be done.  

The second way of looking at work is to change the speed (not the velocity) of an object.  This idea of work where positive and negative makes the most sense.  Positive work is an attempt to speed and object up, negative work is an attempt to slow an object down.  It is very important to understand that it is not velocity we are talking here but only speed.   So positive work does not create a larger positive velocity, and negative work does not create a smaller positive velocity.

You have signed up for a experiment in perception.  You are shown a series of pictures.  The first picture is of a rocket sled on a frictionless track, the rockets on the back have been fired.  The caption under the pictures says " at time equal zero the rockets are fired pushing the crate to the right (the positive x direction)".  The second picture shows the rocket sled 100 meters down the track the rockets are still on.  The caption under the picture says "after 2 secs the sled has traveled 100m to the right (in the positive x direction)".  

The Question is asked:  "Based on the pictures do you expect the sled to be moving slower or faster?"    What do you think? 

Force on the Rocket sled

Displacement of the rocket sled 

   Most of us would believe that the sled would be going faster, and as long as there is no tomfoolery, you would be right.  

Positive work

Force on the Rocket Sled 

Displacement of the Rocket Sled 

 Consider this, if you were shown two simular pictures but instead the rocket sled is pushed to left and after 2 seconds the sled has moved 100m to the left and you are asked the same question how would you respond? 

Most of us would say that the sled would be moving faster, an once again if no trickery, you would be right.  

Both the of these situations are examples of positive work, when considering weather its positive work both the force and displacement vectors must be pointing in the same direction.  

To stress the point even more if you drop and object off the cliff, force of gravity is down and the displacement is down (after a second or two its moved down a few meters), and the object has sped up.

Now the next set of pictures.  The first picture is of a rocket sled on a frictionless track, the rockets on the back have been fired.  The caption under the pictures says " at time equal zero the rockets are fired pushing the crate to the right (the positive x direction)".  The second picture shows the rocket sled 100 meters down the track, the rockets are still on.  The caption under the picture says "after 2 secs the sled has traveled 100m to the left (in the negative x direction)".  

The Question is asked:  "Based on the pictures do you expect the sled to be moving slower or faster?"    What do you think? 

This is a little harder to figure out, what if the first picture had an added caption "the rocket sled has a velocity of 100 m/s to the left (the negative x direction)"?  Well I hope you understand that the rockets are being used to brake the moving sled, to slow it down. 

This in negative work, when the vectors for force and displacement are pointing in the opposite direction it produces negative work.

Force on the Rocket Sled

Displacement of the Rocket Sled 

Negative Work 

Important Equations

Work = F d