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 walk 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

• Ex. calculations- page 393• Units for PE: Joules (J)

– A joule is a kg-m2 / s2

Calculations with PE= mgh

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=(120kg)

(9.8m/s2)(42m)=4.9x104J

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– See math skills pg 395

**Note: if you double the mass, it doubles the KE. If you double the velocity, it will QUADRUPLE the KE

KE= ½ mv 2

Practice Problem• Calculate the kinetic energy in joules of a 1500kg car

moving at the following speeds:i. 29m/sii. 18m/s

iii. 42km/hr EXTENSION- • 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/sKE=(1/2)(1500kg)(18m/s)2=2.4x105J

If the speed was 42 km/hr

• 42 km/hr = 11.66666 m/s• ½ (1500 kg) (11.7m/s)2

= (750 kg) (136 m2/s2)= 1.0 x 10 5 joules

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?

2 /

2(190 ) / 35 /3.3 /

v KE m

v J m sv m s

One more distinction about Energy Types

Mechanical vs

Nonmechanical

Mechanical vs Nonmechanical Energy (write somewhere on your notes- no blanks!)

1. Mechanical Energy- Mechanical Energy is the energy that an object has due to is motion or position, this can be either kinetic energy or potential energy.

* Hint: If something has mechanical energy you can see it move (or you would see it move if it only has potential energy)

Non-mechanical Energy- All the other types–Exs-

•Chemical•Light•Thermal (Heat)•Nuclear•Electromagnetic

Hint: You cannot usually “see” non-mechanical energies

Work

• W= F x D• Work= Force x Displacement• Units- in joules

• Work Energy Theorem- work is equal to the change in energy

• W= DE