WORK AND ENERGYCHAPTER 4

Concept: Mechanical Work

DistanceForce

Object (Mass)

W = Fd

Section 4.1

No Displacement

W = F x 0

Section 4.1

With Displacement, Work!

What Forces?• Gravity

Earth’s gravity Gravity between any two objects

• Electrical (Chapter 8)

• Contact forces Billiard balls colliding Guy pushing crate Hulk throwing guy Tires on the road in accelerating your car

Section 4.1

Mechanical Work

Work againstfriction

Work againstGravity

(Think Newton’s Third Law!)

Mechanical WorkWork done by gravity

Ye Olde Grist Mill Falling Objects

Mechanical WorkWork done in accelerating an object

Section 4.1

Work - Units

SI System (mks)

W = Fd : newton x meter = N-m = joule (J)

British System (fps)

W = Fd : pound x foot = foot-pound (ft-lb)

Work! The Refrigerator

h = 1.35 m

m = 85 kg

Workers lift a crate with a refrigerator in it onto the backof a truck. How much work is done?

Work! The Refrigerator• Knowns

m, mass h, distance

• Unknowns w, weight, or force of gravity W, work

W = FdW = whW = mgh

W = 85 kg( ) 9.8 m/s2( ) 1.35 m( )W = 1120 J

Work! The Refrigerator

F = 450 N

Ff = 450 N

d = 7.5 m

Workers push the crate from the back of the truckto the front a distance of 7.5 m with a force of 450 N. How much work is done?

Work! The Refrigerator• Knowns

F, force d, distance

• Unknowns W, work

W = FdW = 450 N( ) 7.5 m( )W = 3400 J

Work! The RefrigeratorWhen the workers arrive at their destination, they decideto put the crate on a dolly and role it to the back of thetruck. They lift the crate 15 cm to the dolly and pushwith a force of only 25 N to move the crate to the back.

F = 25 N

Ff = 25 N

d = 7.5 m What total workdid they dolifting and movingthe crate?

h = 15 cm

Work! The Refrigerator• Knowns

F, force against rolling frictiond, distance movedh, height liftedm, mass of crate

• UnknownsWl, work lifting the crateWr, work rolling the crateWtot , Total work

Wl = wh = mgh = 85 kg( ) 9.8 m/s2( ) 0.15 m( ) = 125 J

Wr = Fd = 25 N( ) 7.5 m( ) = 188 J

Wtot = 125 J +188 J = 315 J

Compare this result to the work required to slide the crate

Work! The RefrigeratorUnfortunately, the workers have too much fun pushing the crate and, because of its substantial inertia, it keeps going of the end of the truck and smashes onthe pavement. The crate is damaged.

Ultimately, where did the energy come from to damagethe crate?

A. The speed of the crate as it left the truck.

B. The work the workers did in lifting the crate ontothe truck in the first place.

Potential EnergyPotential Energy - the energy an object has because of its position or location, the energy of position

Most potential energy is due to gravity

Remember that: Work = Force x distance (W = Fd)Weight is a force (w = mg)Substitute h (height) for d

Therefore W = mgh Gravitational potential energy = weight x height

Ep = mgh

Section 4.2

Kinetic Energy: Energy of Motion

Ek is kinetic energym is the moving object’s massv is the moving objects speed

Section 4.2

Ek =12mv2

If an object is already moving:Work = change in kinetic energy

W = ΔEk =12mv2

2 − 12mv1

2

W = ΔEk =12m v2

2 − v12( )

Change in Kinetic Energy – an Example

A 1.0 kg ball is fired from a cannon. What is the change in the ball’s kinetic energy when it accelerates from 4.0 m/s to 8.0 m/s?

GIVEN: m = 1.0 kg; v1 = 4.0 m/s; v2 = 8.0 m/s

ΔΕk = Ek2 – Ek1 = ½mv22 - ½mv12

ΔEk = ½(1.0 kg)(8.0 m/s)2 – ½(1.0 kg)(4.0 m/s)2

ΔEk = 32J – 8.0J = 24J

Section 4.2

Other examples ofPotential Energy would include:

Section 4.2

Springs (compressed or stretched)

Bowstring

Conservation of Energy

Let z be height of pendulumabove height zero. zmax = h

Eh = mgh

E0 =12mv0

2

h

0z

Conservation of Energy

Etot = mgz +12mvz

2

• Energy is not a substance

• Energy is a calculation, an invariant of a system

• Energy has application in all aspects of all physicaland biological science.EcologyEvolutionAll physical sciences

Conservation of Energy

• Energy can neither be created nor destroyed.

• In changing from one form to another, energy is always conserved

• The total energy of an isolated system remains constant

• The total energy does not change with time

Section 4.3

Homework- Chap 4

Page 102 & 103 Exercises:

4.1-2, 4.1-4, 4.1-54.2-9, 4.2-12, 4.2-134.3,17, 4.4-21, 4.4-23