BIG IDEA: Work is only present when a force is applied to an object and that object moves: No movement = no work. This class will primarily focus on work done in ONE direction.

Work can be positive or negative:

• depending on whether the force applied to an object adds energy to the object (positive) or takes away energy from an object (negative). Kahn Academy (as usual) explains this well.

• always consider the source of the force (see HERE):

  • Gravity does positive work on your $215 physics book when you push it off the table (ouch!) because the force (mg) is acting in the direction of the displacement (downwards) the book exerieces.

  • You do positive work on the book (with regards to the book) when add energy to the book by lifting it. Our book discusses this in terms of the the book-you system.

  • You do negative work (with regards to gravity) by lifting the book against gravity. Our book describes this in terms of the entire earth-book-you gravity system.

Formulae:

1) W = Fx (where F is a force applied in the x direction and the object moves a distance of x meters)

2) W = Fcosθ (where F is a variable force applied in the x direction and the object moves a distance of x meters, so angle <> 0)

3) W = ∫F dx (where F is a variable force applied in the x direction and the object moves a distance of x meters, so angle = 0)

4) W = ∫F cosθ dx (where F is a variable force applied at an angle θ to the x direction and the object moves a distance of x meters)

5) Kinetic Energy work theorem: W = ∆KE.

Notice that we can also determine a relationship between work and potential energy. KE and Potential Energy are always opposite.

Consider gravitational potential energy: Let's say we use a wrist rocket sling shot to launch a rock upwards with 100. J of kinetic energy. That object comes to a rest at its max height (momentarily) where it now has 100.J of Potential energy. Notice that gravity did work AGAINST the motion of that rock so the work done on that rock by gravity is negative as it accumulated gravitation potential energy (U). Mathematically we can say that:

-W = ∆U

for that situation althoug we commonly write that as:

-W = ∆U

Consider potential energy of a spring: Let's say we compress a spring to the point where it is storing 100. J of potential energy by applying a force through a distance. We know that when we release that spring, it will extend in the opposite direction applying work on any object that way.

W = -∆U

Our good friends at Georgia State University (as is often the case) have a very good mathematical description of our various work formulae. Check out hyperphysics