1. Work and Energy January 30, 2009 Michael F. McGraw, Ph.D.

2. The Concept of Work Many commonly used words have very specific meanings in Physics Work is one of those. Work = Force Displacement The operation is a “Dot Product” that combines two vectors and produces a scalar. The units of Work are those of energy (Joules)

3. Kinetic Energy The Energy of Motion Kinetic Energy is a scalar and in addition cannot be negative V In the absence of net external forces - velocity is constant and therefore so is the Kinetic Energy. - Newton’s 1 st Law

4. Kinetic Energy Changing the Kinetic Energy VfVf F To change the kinetic energy of the system we need to change V. This requires an external force F (F=ma; Newton’s 2 nd Law)

5. Work Changing the Kinetic Energy VfVf F VoVo d W = Work = Fd

6. Starting with the following two equations we can derive the same relationship: V f = V o + at and d = V o t + (½) at 2 Solve the first eqn for t and substitute into the second eqn. V f 2 = V o 2 + 2ad Replace a = F/m, multiply both sides by m/2 and rearrange (½) mV f 2 - (½) mV o 2 = Fd From kinematics the combination of variables (½) mV 2 is seen to be interesting. Work An Approach from Kinematics

7. Work Changing the Kinetic Energy W = Work = VfVf F VoVo d Θ F┴F┴ F ll Only the force component parallel to the motion contributes to work

8. Kinetic Energy Changing the Kinetic Energy VoVo F What happens to the kinetic energy of the system when the force is applied in the opposite direction?

9. Kinetic Energy Changing the Kinetic Energy VfVf F The acceleration will be in the opposite direction and the system (the block) will slow down. V f will be less than V o

10. Work Negative Work - System Energy Reduced VfVf F VoVo d

11. Work The Sign of Work - Is it positive or is it negative? It is relative to the system under study. Let the block be the system. If a force is applied to the block and its KE increases then POSITIVE work has been done on the system - The system energy increased. If a force is applied to the block and its KE decreases then NEGATIVE work has been done on the system - The system energy decreased.

12. Work Determining the Sign of Work

13. Work and Energy Summary An applied external force will change the kinetic energy of the system. The change in kinetic energy is the Work done. Only the force component parallel to the direction of motion contributes to the Work. Positive Work increases the system energy. Negative Work decreases the system energy.