5 work energy notes

Work & Energy

In the past…

v, a, x, t How things move, Kinematics F, a, m What makes them move, Dynamics

Now we will look at WHY they move!!! Energy!

Energy The ability to do work.

Work = Force x Displacement

1 Joule = 1 Newton x 1 Meter

(jewel)

1. Object must move.

2. Force & Displacement must be on the same plane

3. Don’t forget air friction is negligible.

Positive energy is + if it is going into the object/system

Negative energy is – if it is coming out of the object/system

Anything that puts a force on an object displacing it will cause work.

Which of the following do work on the box?

gravity

normal force

you pulling it

friction

No. Doesn’t move up or down

No. Doesn’t move up or down

Yes, but only the x component

Yes

How much work will the road do on an 1800 kg car when its brakes are applied, if the coefficient of friction between the road and the wheels is 0.5 and the car skids 6 m?

W = F d = Ff d = Fg d = m g d

= (0.5) (1800) (9.8) (6)

W = -52, 920 J

F

d

F vs d

Constant ForcesHow do you find work on

F vs d graph?Work = F d

= Area under the curve

Nonconstant forcesΔW = F Δd W = F ∫d

F

d

F vs d

Gravitational Potential Energy energy due to positionPE = mgh

Ex. You lift a 1.2 kg book from the first floor to your social studies class on the 2nd floor 5 m up. How much potential energy does the book have?

PE= m g h = (1.2) (9.8) (5) = 58.8 J

How much work did you do? Conservation!!!

W = PE = 58.8 J

Kinetic Energy energy due to motion

KE = ½ mv2

Ex. How much KE does an 1800 kg car going 25 mph (11.2 m/s) have?

KE = ½ mv2

= ½(1800)(11.2)2

= 113 000 J

How much work would friction need to do to stop it?

W = KE = -113 000 J

Law of Conservation of Energy Energy cannot be created or destroyeda. How much potential energy does it have?

b. How much work was done to get the cart to the top of the first hill?

c. How fast is it going at the bottom of the first hill?

d. If the second hill is 40 m high, then how fast will the cart be going when it crests the hill?

All the energy in = All the energy outW + PE + KE = PE + KE (+W)(Work out is done by friction. If no friction, then no work out.)

A 600 kg roller coaster car is lifted A 600 kg roller coaster car is lifted to the top of the first hill, 55 m to the top of the first hill, 55 m above the ground.above the ground.

PE = m g hPE = m g h

W = PEW = PE PE = KE = ½ mvPE = KE = ½ mv22

PE = PE + KEPE = PE + KE

Sample ProblemA disgruntled physics student drops her book off a 4 story building (12 m), how fast is the book going before it hits the ground?

h = 12 mm = 1.7 kg

Energy in = Energy out

PE + KE = PE + KE

Double check with kinematics!

h = 12 m

Describe the energy transfer in the following Different Scenarios

• Dropping an object off a building

• Throwing an object off a building

• Car being slowed down by friction

• You throwing a ball

• A bullet shot; then embedded in a tree

• You lifting your backpack up to math

Work Energy Theorem

W = ΔKE W = ΔPE

In order to change any type of energy,

work must be done.

Power = Work/Time

Tells you how much energy you use in a certain amount of time.

Metric Unit: Watts

English Unit: Horsepower.

746 Watts = 1 HP

A school bus pulls into an intersection. A car traveling 35 km/h approaches and hits a patch of ice. The driver locks the brakes causing the car to slide toward the intersection. If the car is originally 26 m away and the coefficient of friction between the car’s tires and the icy road is 0.25, does the car hit the bus and poor innocent school children lose their lives … or does the car stop just in the nick of time letting the little children grow up to do physics problems involving school buses and icy roads?

Variable Forces

Springs

Xi Xf

FS F

FS F

Force the spring applies is directly proportional to how far it is stretched.F x F = k x

k is called the spring constantif k is large, spring is stiffif k is small, spring is loose

Hooke’s Law (Robert Hooke)

Energy in a Spring

How would you find the work you put into stretching a spring?

W = F d

But the Force changes over the distance…

So let’s find the average force… When you do work on a

spring, where does that energy go?

Potential Energy!!!

W = PEs = ½kx2

2

122 2 2

1( )212

iF F F kxF kx

W Fd kx x

W kx

Sample ProblemA woman weighing 600 N steps on a bathroom scale containing a spring. The spring is compressed 1.0 cm under her weight. Find the force constant of the spring and the total work done on it during compression.F = kx

k = F/x = 600/0.01 = 60,000

N/mW=½ kx2=½ (60,000) (0.01)2

W = 3.0 Nm = 3.0 J

Garage DoorA large garage door spring is stretched a

distance of 2.50 m when a force of 160 N is applied. Find:

a. the spring constant

b. the work done on the spring

c. the force needed to stretch the spring 1.90 m

d. the power used if the spring is stretched 1.20 m in 3.00 secs.