Types of Energy

Energy is the ability to do work!

• Energy is measured by the amount of work it can do.

Energy comes in different forms…

• Potential energy (PE):– Energy possessed by

an object due to its position

– Sometimes referred to as “stored energy”

Gravitational Potential Energy

• If an object, originally at rest on Earth’s surface, is lifted to some height, work is done against the gravitational force.

• The work done in lifting the object is equal to the objects gravitational potential energy.

work done = gravitational potential energy

W = Fd

Fg

W = mgd

w mg

h

W = ΔPE

ΔPE = mgh

Knowing that the potential energy at the top of the tall platform is 50 J, what is the potential energy at the other

positions shown on the stair steps and the incline?

Path doesn’t matter…

Remember that the changes in an object's potential energy only depend on comparing its starting position and its ending position, not on whether it does or does not pass through various points in-between.

Try this…

• How much potential energy is gained by an object with a mass of 2 kg that is lifted from the floor to the top of a .8 m high table?

ΔPE = mgh

ΔPE = (2kg)(10m/s2)(.8m)

ΔPE =16 J

Try this…• King Kong is on top of the Empire State

Building 426 m above the surface of the Earth. What is his gravitational potential energy relative to the ground? Let’s say his mass is 1000 kg (a metric ton).

ΔPE = mgh

ΔPE = (1000kg)(10m/s2)(426m)

ΔPE = 4,260,000 J

Draw how the graph would look that represents this relationship- PE vs. h

PE

h

ΔPE = mgh

PE = mg h

What if m = .1 kg

Elastic Potential Energy

• Energy can be stored in a spring and is measured as the work required to stretch or compress it.

Remember Hooke’s Law…

• The compression or elongation of a spring is directly proportional to the applied force.

Fs = kxSpring constant

The larger the k, the stiffer the spring.

What’s the spring constant of this spring?

x

F

F = kx

k = F x

= 25 N .50 m

= 50 N/m

Potential Energy of a Spring

W = Fd

W = PEs

½ kx x

PEs = ½ kx2

What would the graph look like that shows this relationship- PE vs. x?

PE

x

PE

x

PE

x

PE

x

PEs = ½ kx2

What if we made k = 2 N/m

PEs = x2

Elastic potential energy can be stored in rubber bands, bungee chords, trampolines,

springs, an arrow drawn into a bow, etc.

Try this…

• A force of 50 N is needed to compress a spring a distance of 1 m. What is the potential energy stored in the compressed spring?

PEs = ½ kx2

PEs = ½ (50)(1m)2Fs = kx

Fs = kxx x

k = Fs x

k = 50 N 1 m

k = 50 N/m PEs = 25 J

Try this…• When a spring is stretched .2 m from its

equilibrium position, it possesses a potential energy of 10 J. What is the spring constant for the spring?

PEs = ½ kx2

k = 2PE x2

k = 500 N/m

Kinetic Energy

• When a moving object strikes another object and displaces it, the moving object exerts a force on the second object and does work on it.

Kinetic Energy- the energy an object possesses due to its motion.

W = Fd

W = ΔKE

ma

vt

vt

from rest- v 2

W = ΔKE = m v v t t 2 ΔKE = ½ mv2

Try this…

• What is the kinetic energy of a 980 kg race car traveling at 90 m/s?

ΔKE = ½ mv2

ΔKE = ½ (980kg)(90m/s)2

ΔKE = 3,969,000 J

Try this…

• Determine the kinetic energy of a 625-kg roller coaster car that is moving with a speed of 18.3 m/s.

ΔKE = ½ mv2

ΔKE = ½ (625kg)(18.3m/s)2

ΔKE = 104,653 J

Try this…• A platform diver for the Circus has a

kinetic energy of 12 000 J just prior to hitting the bucket of water . If the divers mass is 40 kg, then what is her speed?

ΔKE = ½ mv2

v2 = 2KE m

v = 25 m/s