WORK AND ENERGY
CHAPTER 4
Concept: Mechanical Work
Object (Mass)
Force
Distance
W = Fd
No Displacement
W=Fx0
Section 4.1
With Displacement, Work!
Section 4.1
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
Mechanical Work
Work against
friction
Work against
Gravity
(Think Newton’s Third Law!)
Section 4.1
Mechanical Work
Work done by gravity
Ye Olde Grist Mill
Falling Objects
Mechanical Work
Work done in accelerating an object
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)
Section 4.1
Work! The Refrigerator
Workers lift a crate with a refrigerator in it onto the back
of a truck. How much work is done?
m = 85 kg
h = 1.35 m
Work! The Refrigerator
• Knowns
m, mass
h, distance
• Unknowns
w, weight, or force of gravity
W, work
W = Fd
W = wh
W = mgh
W = ( 85 kg ) ( 9.8 m/s
W = 1120 J
2
)(1.35 m )
Work! The Refrigerator
Workers push the crate from the back of the truck
to the front a distance of 7.5 m with a force of 450 N. How much work is done?
d = 7.5 m
F = 450 N
Ff = 450 N
Work! The Refrigerator
• Knowns
F, force
d, distance
• Unknowns
W = Fd
W = ( 450 N ) ( 7.5 m )
W = 3400 J
W, work
Work! The Refrigerator
When the workers arrive at their destination, they decide
to put the crate on a dolly and role it to the back of the
truck. They lift the crate 15 cm to the dolly and push
with a force of only 25 N to move the crate to the back.
d = 7.5 m
F = 25 N
Ff = 25 N
h = 15 cm
What total work
did they do
lifting and moving
the crate?
Work! The Refrigerator
• Knowns
F, force against rolling
friction
d, distance moved
h, height lifted
m, mass of crate
• Unknowns
Wl, work lifting the crate
Wr, work rolling the crate
Wtot , Total work
Wl = wh = mgh = ( 85 kg ) ( 9.8 m/s
2
)( 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 Refrigerator
Unfortunately, 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 on
the pavement. The crate is damaged.
Ultimately, where did the energy come from to damage
the crate?
A. The speed of the crate as it left the truck.
B. The work the workers did in lifting the crate onto
the truck in the first place.
Potential Energy
Potential 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
1 2
Ek = mv
2
Ek is kinetic energy
m is the moving object’s mass
v is the moving objects speed
If an object is already moving:
Work = change in kinetic energy
1 2 1 2
W = ΔEk = mv2 − mv1
2
2
1
2
2
W = ΔEk = m v2 − v1
2
(
)
Section 4.2
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 of
Potential Energy would include:
Springs (compressed or stretched)
Bowstring
Section 4.2
Conservation of Energy
Let z be height of pendulum
above height zero. zmax = h
Eh = mgh
h
0
1 2
E0 = mv0
2
z
Conservation of Energy
1 2
Etot = mgz + mvz
2
• Energy is not a substance
• Energy is a calculation, an invariant of a system
• Energy has application in all aspects of all physical
and biological science.
Ecology
Evolution
All 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, 4.1-5
4.2-9, 4.2-12, 4.2-13
4.3,17, 4.4-21, 4.4-23