Download Energy & Power

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?
vi = ?
1.8 m
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