PHYS 218 sec Review Chap. 6 Work and Kinetic Energy

Work Displacement vector Constant force Straight-line displacement Force and displacement are in the same direction. Unit of work

Work Constant force in direction of straight-line displacement Constant force, straight-line displacement Varying x-component of force, straight-line displacement Work done on a curved path (general definition of work)

Evaluation of Work Ex 6.1 Ex 6.2

Work done by a varying force, straight-line motion mm Work is the area under the curve between the initial and final positions in the graph of force as a function of position.

Evaluation of Work: Stretched spring Restoring force

Varying x-component of force, straight-line displacement Evaluation of Work When F x is constant

Kinetic energy and work-energy theorem Kinetic energy (K) Work-Energy Theorem When v = 0, K = 0 The work done by the net force on a particle equals the change in the particle’s kinetic energy This is a very general theorem. This theorem is true regardless of the nature of the force. Kinetic energy at the initial point Kinetic energy at the final point

Proof of the work-energy theorem Constant force in direction of straight-line displacement mm When a particle undergoes a displacement, it speeds up if W > 0, slows down if W < 0, and maintains the same speed if W = 0.

Proof of the work-energy theorem Varying force, straight-line motion Eliminate time dependence since W is an integral over x.

Ex 6.3 Same as Ex 6.2: suppose that the initial speed v 1 is 2 m/s. What is the final speed? Examples Use Work-Energy Theorem to calculate speed.

Forces on a hammerheadEx 6.4 hammerhead I-beam Point 3 Point 2 Point 1 3 m 7.4 cm Falling hammerhead Speed of the hammerhead at point 2

Forces on a hammerhead Ex 6.4 (cont’d) Hammerhead pushing I-beam i.e., Point 2  Point 1 Work-energy theorem Using the previous result Be careful with the change of unit

Motion with a varying forceEx 6.7 m Friction (  k )

Ex 6.8Motion on a curved path I

Ex 6.9Motion on a curved path II (another way to compute the line integral) We get the same answer as in Ex 6.8

Power Average power The time rate at which work is done. (Instantaneous) power Unit of power Writing power in terms of F