8. Machines Machines can change the direction of a force and/or multiply the force. Work comes in two forms: input and output Work input (W in ) = F effort ·x effort Work output (W out ) = F resistance ·x resistance

9. Mechanical Advantage Mechanical Advantage (MA): indicates the amount by which the effort force F e is increased by the machine. Dimensionless (no units) Ex: if the MA of a machine is 4, the machine multiplies F e by 4 to get F R ; if F e = 10 N, then F R = 4·10 N = 40 N. MA does take friction into account. The MA of a pulley is equal to the number of ropes that support weight.

10. Efficiency Efficiency: the ratio of work output to work input.

11. Efficiency Efficiency is always less than 1 (as a decimal) or 100% due to frictional losses. The higher the efficiency, more of the work input is converted to work output; less of the work output is lost to overcoming friction.

12. REVIEW: WORK SPRINGS INCLINES

13. Spring (Elastic) Constant k F = -k·  x (this equation is called Hooke’s law)  x = distance of stretch/compression k = spring constant; unit = N/m. The spring constant is a measure of the stiffness of the spring; the larger k is, the stiffer the spring is (and the more force is needed for a given displacement) Negative sign indicates that the force F of the spring is in the opposite direction to the distorting force (the pull or the push on the spring). In the problems you will solve, the negative sign is often dropped. The force F is always directed toward the equilibrium position. Work = 0.5·k·  x 2

14. Elastic Objects/The Spring Force We know from common experience that the harder you push on a spring, the harder it pushes back; the same is true for pulling… The force needed to stretch or compress an elastic object is a varying force, increasing with increasing distance from the equilibrium position (the unstretched position, where x = 0).

15. Work and Inclined Planes F x = gravitational component W = F x·  x The direction of motion is positive. F x is negative if the object moves up the incline. F x is positive if the object moves down the incline.

16. Things To Look For Pulling an object with friction: flat surface Work done by the pulling force F:  W = F x ·x  Work done by friction: W = -F f ·x