Kinetic and Potential Energy
Energy and Work are closely related
• Work is a transfer of Energy
– SI unit for work is Joules (J)
• Energy is the capacity to do Work
– We recognize it by the changes it causes
We use energy to carry a backpack upstairs.
(work)
Kinds of Energy
1. Potential Energy(PE)
• the energy that an object has because of its position,
shape or condition.
Potential Energy of Position
• PE depends on an objects mass, height, and the
acceleration due to gravity.
PE= mgh
Kinds of Potential Energy
• Potential Energy of Position (Gravitational PE)
– Figure 11, page 392: the apple has potential
energy that results from the gravitational
attraction between the apple and earth
Kinds of Potential Energy
• Elastic Potential Energy
– The PE of an object that is stretched or
compressed
• Ex- stretching a rubber band or bouncing a basketball
Calculations with PE= mgh
• Ex. calculations- page 393
• Units for PE: Joules (J)
– A joule is a kg-m2 / s2
Practice Problems
• Calculate the gravitational potential energy in
the following systems:
– A car with a mass of 120 kg at the top of a 42 m
hill
– A 65 kg climber on top of Mt Everest (8800 m
high)
– A 0.52 kg bird flying at an altitude of 550 m
A car with a mass of 120 kg at the top of a
42 m hill
PE=mgh=(1200kg)(9.8m/s2)(42m)=4.9x105J
a 65 kg climber on top of Mount
Everest (8800m high)
PE=(65kg)(9.8m/s2)(8800m)=5.6x106J
a 0.52kg bird flying at an altitude of
550m
PE=(0.52kg)(9.8m/s2)(550m)=2.8x103J
Another Problem
• A science student holds a 55g egg out a
window. Just before the student releases the
egg, the egg has 8.0 J of gravitational potential
energy with respect to the ground. How far is
the student’s arm from the ground (in
meters)?
Answer
• h= PE/mg = 8.0J/(0.055kg)(9.8m/s2)=15m
Another Problem
• A diver has 3400J of gravitational potential
energy after stepping up onto a diving
platform that is 6.0m above the water. What is
the diver’s mass in kilograms?
Answer
• m=PE/gh=(3400J)/(9.8m/s2)(6.0m)=58kg
Kinetic Energy (KE)
• The energy of a moving object due to the
object’s motion
– The KE of any moving object depends on its mass
and velocity
2
– See math skills pg 395
KE= ½ mv
**Note: if you double the mass, it doubles the KE.
If you double the velocity, it will QUADRUPLE the
KE
Practice Problem
• Calculate the kinetic energy in joules of a 1500kg
car moving at the following speeds:
i. 29m/s
ii. 18m/s
iii. 42km/s
• A 35kg child has 190J of kinetic energy after
sledding down a hill. What is the child’s speed in
meters per second at the bottom of the hill?
Answers
• Calculate the kinetic energy in joules of a 1500kg
car moving at the following speeds:
• i. 29m/s
KE=1/2mv2=(1/2)(1500kg)(29m/s)2=6.3x105J
• ii. 18m/s
KE=(1/2)(1500kg)(18m/s)2=2.4x105J
• ii. 42m/s
KE=(1/2)(1500kg)(42m/s)2=
Answer
• A 35kg child has 190J of kinetic energy after
sledding down a hill. What is the child’s speed
in meters per second at the bottom of the
hill?
v  2 KE / m
v  2(190 J ) / 35m / s
v  3.3m / s