Chapter 7 - Work and Energy
• Work
– Definition of Work [units]
– Work done by a constant force (e.g friction,weight)
– Work done by a varying force (e.g. a spring)
– Work in 3 dimensions – General Definition
• Work and Kinetic Energy
– Definition of Kinetic Energy
– Work-Energy Principle

• Work - The means of transferring energy by the application of a force.
• Work is the product of the magnitude of displacement times the component of that force in the direction of the displacement.
• Work is a scalar
• Energy - The state of one or more objects. A scalar quantity, it defines the ability to do work.
W

F
//
 
F
 r cos


Physical
Quantity
Length
Dimension
Symbol
[L]
Mass [M]
SI MKS SI CGS m kg cm g
US
Customary ft slug
Time
Acceleration
[T]
[L/T
2
] sec m/s
2 sec cm/s
2 sec ft/s
2
Force [M-L/T
2
] newton (N) kg-m/s
2
Energy [M-L 2 /T 2 ]
Joule (J)
N-m kg-m 2 /s 2
Dyne g-cm/s
2
Erg
Dyne-cm g-cm 2 /s 2 pound (lb) slug- ft/s
2
Ft-lb slug-ft 2 /s 2

• A 1500 kg car accelerates uniformly from rest to a speed of 10 m/s in 3 s.
• Find the work done on the car in this time
W

F
//
 
F
 r cos


How much work is done by this guy?
Walking at a constant speed
 r
W

F
//
 
F
 r cos


• m = 50 kg
• displacement = 40 m
• force applied = 100 N
• 37 o angle wrt floor
• m k
= 0.1
• Find net work done moving the crate

Vector Multiplication – Scalar Product
A

A i x
ˆ 
A j A k y
ˆ  z
ˆ
B

B i x
ˆ 
B j B k y
ˆ  z
ˆ
A B

A B cos

  ˆ ˆ 
1
  ˆ ˆ 
0
A B

A B x x

A B y y

A B z z

A more elegant definition for work
W

F
//
 
F
 r cos

A B

A B cos

W F r

• How much work is done pulling the wagon 100 m in the direction shown by the boy applying the force:
ˆ
 r


W
1

F cos
1
  l
1 1
W
 lim
 
0
7 
F cos i
   i i
 a b
W

7 
F cos i
  l i i
   a b 

F

F i x
ˆ 
F j F k y
ˆ  z
ˆ dr
 dxi
ˆ  ˆ  ˆ
W
  a b    x x a b
F dx x
  y a y b
F dy y
  z z a b
F dz z

F x
(N)
3
2
1
5 10 15 x (m)
How much work is done by this force?

Hooke’s Law and the work to compress/extend a spring
F s
  kx
W
  a b    x x a b
F dx x
W
P
  x b
 x x a

0
  
1
2 kx
2

Kinetic Energy and the
Work-Energy Principle
W

F d
 m a d
 m v
2
 v
2
0
2d d

1
2 mv
2 
1
2 mv
2
0
W
 
0
 
K
K

1
2 mv
2

And you can show this with calculus too!
W
  a b    x x a b
F dx x
 
1
2 dv
    
1
W m dx m dv mvdv mv dt 1
2 dx dt 1
2
2
2
2

1
2 mv
1
2

• A 3 kg mass has an initial velocity, v = (5 i - 3 j ) m/s.
• What is the kinetic energy at this time?
• The velocity changes to (8 i + 4 j ) m/s.
• What is the change in kinetic energy?
• How much work was done?

• A 2 kg block is attached to a light spring of force constant
500 N/m. The block is pulled 5 cm to the right and of equilibrium. How much work is required to move the block?
• If released from rest, find the speed of the block as it passes back through the equilibrium position if
– the horizontal surface is frictionless.
– the coefficient of friction is 0.35.