Chapter 7 - Work and Energy • Work

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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

Definitions

• 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

Units

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

Problem 1

• 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

Problem 3

• 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

Problem 4

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

ˆ

 r

Work done by a varying force

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 

Work in three dimensions

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

Problem 5

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

Problem 6

• 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?

Problem 7

• 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.

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