Work, Power, and Energy

Work In order for an object to move, a force must be exerted Amount of work done depends on the amount of force exerted and how far the object moves

Work (cont.) W = F d Work: the product of the force exerted and the distance the object moves W = F d

ex. A force of 50 newtons is used to drag a crate across the floor at constant velocity. How much work is done to drag the crate 8.0 m? W = F d = ( 50 N )( 8.0 m ) = 400 N m = 400 joules = 400 J James Joule (1818 – 1889) Def’n: 1 joule = 1 N m

ex: (a) How much work is done to lift a bowling ball of mass 7.0 kg to a height of 1.5 m? F W = F d To lift an object, must exert force equal to the weight F = Wt. = m g = ( 7.0 kg )( 9.8 m/s2 ) Wt. = 68.6 N W = F d = ( 68.6 N )( 1.5 m ) = W = 103 J

* (b) How much work is done to hold it up? Zero, since there is no displacement (c) How much work is done to carry it horizontally a distance of 3.0 m? Zero * The displacement must be in the direction of the exerted force in order for work to be done Exerted force is vertical (against gravity) ; displacement is horizontal (no vertical displacement) so Work done = 0

ex: A sled is pulled along the ground by a rope that makes a 25o angle with the horizontal. The tension in the rope is 20 N. Find the work necessary to drag the sled 52 m. 20 N Displacement is horizontal; find component of force in the horizontal direction 25o 52 m

ex: A sled is pulled along the ground by a rope that makes a 25o angle with the horizontal. The tension in the rope is 20 N. Find the work necessary to drag the sled 52 m. 20 N Displacement is horizontal; find component of force in the horizontal direction 25o Fh 52 m W = F d Fh cos 25 = = Fh d 20 = ( 18.1 N )( 52 m ) Fh = 20 cos 25 W = 943 J Fh = 18.1 N

ex. A refrigerator weighs 2000 N. How much work would be done to lift it onto a truck bed 1.5 m above the ground? W = F d = ( 2000 N )( 1.5 m ) = 3000 J Problem: I cannot lift 2000 N Need to use a machine

I can use a ramp to lift the 2000-N refrigerator onto the truck. The ramp is 6 m long, and I push it up. F = 500 N 1.5 m 6 m This is supposed to be a truck? I find that I only have exert a force of 500 N to push the refrigerator up the ramp. But I have to exert that force over a greater distance.

The amount of work done to push the refrigerator up the ramp is F = 500 N 1.5 m 6 m This is supposed to be a truck? The amount of work done to push the refrigerator up the ramp is W = F d = ( 500 N )( 6 m ) = 3000 J This is the same amount of work as to lift the refrigerator straight up. So the ramp did not “save us work”; the same amount was done in either case

ex. A barbell weighs 800 N. Tom lifts it to a height of 2.0 m and holds it there. (a) How much work is done to lift it? W = F d = ( 800 N )( 2.0 m ) = 1600 J (b) How much work is done to hold it up? Zero; if the barbell does not move, no work is done

Tom lifts it to that height in 2.0 s. His friend Pete lifts it also, but takes 3.0 s to do it. Which guy is stronger? Tom exhibits more power

Power: the time rate of doing work If you do the same amount of work in a shorter time, you exhibit more power

ex. Sue lifts a 300-N weight to a height of 2.0 m in 3.0 s. (a) How much work did she do? W = F d = ( 300 N )( 2.0 m ) W = 600 J (b) How much power did she exert? W 600 J P = = t 3.0 s = 200 J/s = 200 watts = 200 W James Watt ( 1736-1819 ) Def’n: 1 J/s = 1 watt

Energy : the ability to do work Examples:

Potential Energy: energy of position Forms of PE: - gravitational elastic ( bowstring, rubber band ) - chemical ( TNT, food ) - nuclear ( stars )

Work-Energy Theorem: the energy acquired by a body is equal to the work done on it Apply to Gravitational Potential Energy: PEg = Work done to lift object = F d Force to lift = weight = Wt. d = m g d Gravitational PE of object lifted to height h PEg = m g h

Kinetic Energy: energy of motion Work can also be done to cause an object to obtain motion Kinetic Energy: energy of motion Depends on: -speed (pitched baseball) -mass (bowling ball)

Apply Work-Energy Theorem to Kinetic Energy: KE = Work done on object = F d = ma d vf2 = vi2 + 2 a d = m ( a d ) start from rest: vi = 0 vf2 = 2 a d KE = m ( ½ vf2 ) 2 2 ½ vf2 = a d KE = ½ m v2

Which object has potential energy but no kinetic energy?

Which object has kinetic energy but no potential energy?

Which object has both potential energy and kinetic energy?

Conservation of Energy: The total amount of energy in an isolated system remains constant. Total Energy = Potential Energy + Kinetic Energy Tot. En. = PE + KE

Rube Goldberg Machine Project A Rube Goldberg machine is a series of simple machines connected to perform a task The Self-Operating Napkin: As you raise spoon of soup (A) to your mouth it pulls string (B), thereby jerking ladle (C) which throws cracker (D) past parrot (E). Parrot jumps after cracker and perch (F) tilts, upsetting seeds (G) into pail (H). Extra weight in pail pulls cord (I), which opens and lights automatic cigar lighter (J), setting off sky-rocket (K) which causes sickle (L) to cut string (M) and allow pendulum with attached napkin to swing back and forth thereby wiping off your chin.

Task: Flip a light switch upward to turn on a bulb Must fit on a base 1 m x 1 m Must consist of at least five distinct steps Must contain at least three different simple machines; more gets extra credit All parts must remain on base No live animals No explosions, although fire may be allowed Must be able to reset and run again in 5 minutes Nothing may be plugged in, although battery-powered objects are ok

Rubric for Rube Goldberg Project Success in the Objective 4 6 8 10 12 20 At Least Five Steps 1 2 3 4 5 Machine Made in Class 1 2 3 4 5 On Time/Taken Home 1 2 3 4 5 6 7 8 9 10 Elegance of Design 1 2 3 4 5 6 7 8 9 10    Total: __________ x 1.5 = __________ Points from individual evaluations (25 max.) = ______   Total = _________