6 Work and Kinetic Energy Work Done by
6 Work and Kinetic Energy • Work Done by a Constant Force • Work Done by a Variable Force – Straight Line Motion • The Scalar Product • Work-Kinetic Energy Theorem – Curved Paths • Hk: 27, 41, 49, 51.
Some Definitions Energy: The work that a physical system is capable of doing in changing from its actual state to a specified reference state … (American Heritage Dictionary) Energy: The capacity to do work. (Physics) What is Work?
Work Transformation • Work is a usage of energy, e. g. , • Burning gasoline produces heat & motion • battery running a car • /
Work • Work is force x distance (N·m = joule), force parallel to motion (no work done by perpendicular component) • It takes energy to do work. • Less stored energy is available after productive work is done.
Work by Constant Force Ex: F = 80 N, Angle is 40°, Dx is 11 m, Work = Fcosq. Dx = (80 N)(cos 40)(11 m) = 674 J
Total Work on Object
Kinetic Energy
Example: 20 kg moving at 5 m/s. 250 J of work (total) are done on it. What is its final speed?
Negative Work (object slows down) Ex. A car moves 10 meters while a braking force of 500 newtons acts.
Ex. Block pushed 3 m with 75 N of force while Friction of 50 N. Total Work is,
Work by a Variable Force, Straight Line Motion
Hooke’s Law • Elastic restoring force proportional to deformation • F = -kx k = elastic constant (N/m) • Ex. Lab springs, k = 8 N/m, 0. 1 kg mass: • mg = kx • (0. 1 kg)(9. 8 N/kg) = 8 N/m(x) • x = 0. 98 N/(8 N/m) = 0. 1225 m
Scalar (Dot) Product
Example: Find the angle between A = (1, 1, 1) and B = (5, 0, 0)
Power
Ex: A car drives at 20 m/s and experiences air-drag of 400 N.
What size motor needed when Operating Speed is 10 cm/s? Cube of bricks ~ 1 ton = 2000 lbs ~ 9000 N Minimum Power: P = Fv = (9000 N)(0. 1 m/s) P= 900 W = 1. 2 hp
Work along Curved Path
Summary • Work is force parallel to path x distance (force constant) • Negative total work (object slows down) • Work is integral of force·distance (Scalar Product) • Power is rate work is done • Total work = change in KE • /
- Slides: 21