Energyand 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 = ½mvf

2 + 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