1. Chapter 5: Work & Energy The Work/Energy Relationship

2. Work done by a constant net force: W = F x ∆x For forces applied at an angle, θ: W=Fcosθ d “d” is the magnitude of displacement

3.  Work is only done when a force causes an object to move some distance.  Work is measured in units called Joules (J).  Work is a scalar quantity that can be positive or negative.

4. Positive work results in a displacement in the same direction as the applied force. Work is negative when the force is opposite the displacement. F net Displacement F net Displacement Friction is doing negative work on the box. FkFk

5. Work done by friction: W f = F k Δx

6. Applying force at an angle can alter the frictional force. Reduction of frictional force because F y is upward, and reduces the normal force. Increase of frictional force because F y is downward, and increases the normal force. FyFy FyFy

7. Net Work Done on an Object: W net = ∆KE = ½mv 2 – ½mv 0 2 Kinetic Energy of an Object: KE = ½mv 2

12. Gravitational Potential Energy: PE = mgy *Can also be expressed as “weight x height” Work done by gravity: W g = -( PE f – PE i ) = -( mgy f – mgy i )

13. Suppose that friction (or some other nonconnservative force) does work on a mechanical system: For example – a firefighter sliding down a pole to reach the first floor. Work done by a nonconservative force: W nc = ΔKE + Δ PE

14. Conservation of Mechanical Energy: KE i + PE i = KE f + PE f If gravity is the only force doing work: ½mv 2 i + mgy i = ½mv 2 f + mgy f