Lecture 11: Potential Energy &

Energy Conservation

Questions of Yesterday1) You slam on your brakes in a panic and skid a certain

distance d down a straight and level road before coming to a stop. If you had been traveling twice as fast, what would the skidding distance be? a) 2d

b) d/2c) 4dd) d/4

2) As a pendulum swings back and forth, the forces acting on the pendulum are the force of gravity and tension in the supporting cord. Which of these forces does no work on the pendulum?a) Gravityb) Tensionc) neither one does work on the pendulumd) they both do work on the pendulum

Gravitational Potential EnergyThere is a 10 m high and a 2 m high diving board. You

know that the faster you are going when you hit the water the bigger splash you will make. Which board

will you jump off of to make the biggest splash?

Which board gives you the greatest kinetic energy when you hit the water?

Is work done on you as you fall?How do you know?

What is doing work on you?

The higher up you are the greater the potential you have to gain kinetic energy by gravity doing work on

you

Gravitational Potential Energy

Potential energy is the property of a system with a set “zero point” or “ground level”

Potential Energy always refers to some object at some certain point in space relative to the “ground”

Instead of looking at the work done by gravity on an object during any vertical displacement…

we can look at GRAVITATIONAL POTENTIAL ENERGY (PE) or the energy associated with the potential for

gravity to do work on an object

Choosing your reference frame is important!

Gravitational Potential EnergyDoes the work done on an object by gravity increase or

decrease as it falls?

What about the potential energy?

distance fallen (m)

En

erg

y (

J)

Potential EnergyW

ork

done

by

Gravity

Gravitational Potential EnergyDoes the work done on an object by gravity increase or

decrease as it falls?

What about the potential energy?

distance fallen (m)

En

erg

y (

J)

Potential EnergyW

ork

done

by

Gravity

The change in Potential Energy between two

points = The negative of the

work done by gravity through that displacement

Gravitational Potential Energy

What is the work done by gravity on the book from height yi to yf?

yi

yf

Wg = (Fgcosy

Wg = mgcosyi -

yf)PE = -Wg

PE = mg(yf - yi)

Gravitational Potential Energy

PE = mgy

y = vertical distance (height) of an object from the Earth’s surface or some other “zero” point

g = magnitude of acceleration due to gravity

Unitskg*m2/s2 =

Joule (J)Scalar QuantityAlways Positive!

Gravitational Potential Energy

PE = mgy

Recall the work energy theorem…

Wnc + Wc = KE

Wg = mgyi - yf)

Wnc = KE + PE

Reference Levels, y = 0

PE = mgy

When calculating PE you can choose “y = 0” to be at any vertical

height in your system

Only the CHANGE in PE matters!

yi

yf

y = 0

y = 0

Wnc = KE + PE

Energy Conservation

If only conservative forces are acting on a system…Energy is Conserved!

The sum of the kinetic energy and potential energy of an isolated system remains CONSTANT at all times!

Wnc = KE + PE

KEi + PEi = KEf + PEfwhen Wnc = 0

Mechanical Energy

In any isolated system of objects interacting only through conservative forces, the total mechanical

energy E = KE + PE of the system remains the same at all times!

Kinetic Energy (KE) + Potential Energy (PE) = Mechanical Energy (E)

KEi + PEi = KEf + PEf

E = KE + PE

Ei = Ef

Energy Conservation

Energy conservation when gravity is the only conservative force acting on the system

KEi + PEi = KEf + PEf

(1/2)mvi2 + mgyi = (1/2)mvf

2 + mgyf

PE = mgyKE = (1/2)mv2

Practice Problem

Assuming the ramps are frictionless and the balls of equal mass start from rest….

Which ball has a greater speed when it reaches the bottom?

If the ramps have friction (equal coefficients of friction)… would your answers change?

h h

30o 60o

Which ball reaches the bottom first?

Practice Problem

A 70-kg diver steps off a 10-m tower and drops from rest straight down into the water. If he comes to rest 5.0 m beneath the surface, determine the average resistive

force exerted on him by the water.

Practice ProblemStarting from rest, a 10.0 kg block slides 4.00 m down to the bottom of the frictionless ramp inclined 30.0o. The block then slides an additional 5.00 m along the floor

before coming to a stop.

Determine:-The speed of the block at the bottom of the ramp

-The coefficient of kinetic friction between the block and floor

-The mechanical energy lost due to friction

What if the coefficient of friction between the ramp and the block was 0.5?

Questions of the Day1) A 50-kg student starting from rest slides down a

frictionless waterslide of height 10 m while a 100-kg student slides down a similar slide that is only 5 m high. Which student is going faster when they reach the bottom?a) the 50-kg studentb) the 100-kg studentc) they are going the same speed

2) A women pulls a crate up a rough (with friction) inclined plane at a constant speed. Which statement is NOT true?

a) The work done on the crate by the normal force of the inclined plane on the crate is ZEROb) The work done on the crate by gravity is ZERO c) The work done by the net force on the crate is ZEROd) The gravitational PE is increasing