Energy and Power.

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Energy and Power

Kinetic Energy Kinetic Energy is the energy of motion KE = ½mv2 m = mass of object v = speed of object KE is always zero or positive, never negative Net work done on an object results in a change in kinetic energy: Wnet = KE

Potential Energy Potential energy is stored energy An object has potential energy because of its relative position to other objects Only a change in potential energy matters Gravitational potential energy is stored energy because of an objects position relative to earth PEg = mgh h = height above zero level The zero level is arbitrary

Potential Energy (cont.) Elastic potential energy is energy stored in a compressed or stretched object Classic example is a spring: PEelastic = ½ kx2 k = the spring constant x = distance object is stretch or compressed Spring constant (units = N/m) is a measure of how stiff the spring is

Example of Potential Energy How high can a dart gun (k = 100 N/m) shoot a 3.1 g dart, given that the spring is compressed 4.0 cm? Answer: At the highest point, the energy of the compressed spring becomes PEg: ½ kx2 = mgh h = kx2/(2mg) = (100 N/m)(.040 m)2/ [2(.0031 kg)(9.8 m/s2)] = 2.6 m

Conservation of Mechanical Energy Kinetic and potential energy are the two types of mechanical energy The total mechanical energy of an object or group of objects is ME = KE + PE If there is no friction, then ME is conserved: MEi = MEf KEi + PEi = KEf + PEf ½mvi2 + mghi = ½mvf2 + mghf (PEelastic = 0)

Example of Conservation of Mechanical Energy Tarzan is running through the jungle. He grabs a vine to get over a chasm, but the other side is 1.8 m higher. How fast does he need to be running to make it? 1.8 m vi = ?

Power Power is the rate that work is done or energy transferred P = W/t (work per time) or P = Fv (force  speed) The SI unit for power is the watt (W) 1 W = 1 J/s

Example A 120-kg backpacker climbs a 1400-m high mountain in 6.3 hours. What is his power output? W = Fd = mgd P = W/t = mgd/t = (120 kg)(9.80 m/s2)(1400 m) (6.3 h)(3600 s/h) = 73 W

Example A woman lifts a bucket of water out of a well at a speed of 1.75 m/s. The bucket plus water has a total mass of 9.30 kg. What is her power output? P = Fv = mgv = (9.30 kg)(9.80 m/s2)(1.75 m/s) = 159 W

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