chapter 7 - work and energy work –definition of work [units] –work done by a constant force (e.g...
TRANSCRIPT
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 r F r cos
UnitsPhysicalQuantity
DimensionSymbol
SI MKS SI CGS USCustomary
Length [L] m cm ft
Mass [M] kg g slug
Time [T] sec sec sec
Acceleration [L/T2] m/s2 cm/s2 ft/s2
Force [M-L/T2] newton (N)kg-m/s2
Dyneg-cm/s2
pound (lb)slug- ft/s2
Energy [M-L2/T2] Joule (J)N-m
kg-m2/s2
ErgDyne-cmg-cm2/s2
Ft-lbslug-ft2/s2
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 r F r cos
How much work is done by this guy?
Walking at a constant speed
//W F r F r cos
r
Problem 3
• m = 50 kg
• displacement = 40 m
• force applied = 100 N
• 37o angle wrt floor
• k = 0.1
• Find net work done moving the crate
Vector Multiplication – Scalar Product
A B A B cos
ˆ ˆ ˆ ˆ ˆ ˆi i j j k k 1
ˆ ˆ ˆ ˆ ˆ ˆi j i k j k 0
x y zˆ ˆ ˆA A i A j A k
x y zˆ ˆ ˆB B i B j B k
x x y y z zA B A B A B A B
A more elegant definition for work
//W F r 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 ˆF 17Ni 10Nj
r
Work done by a varying force
1 1 1 1W F cos l 7
i i ii 1
W F cos l
i
7 b b
i i i a al 0i 1
W lim F cos l Fcos dl F dl
Work in three dimensions
x y zˆ ˆ ˆF F i F j F k
ˆ ˆ ˆdr dxi dyj dzk
b b b
a a a
b x y z
x y za x y zW F dr F dx F dy F dz
Problem 5
5 10 15 x (m)
3
2
1
Fx (N)
How much work is done by this force?
Hooke’s Law and the work to compress/extend a spring
sF kx
b
a
b x
xa xW F dr F dx
b
a
x x 2P x 0
1W kx dx kx
2
Kinetic Energy and the Work-Energy Principle
2 22 20
0
v v 1 1W F d m a d m d mv mv
2d 2 2
0W K K K
21K mv
2
And you can show this with calculus too!
b
a
b x
xa xW F dr F dx
2 2 2 2 22 11 1 1
dv dx 1 1W m dx m dv mvdv mv mv
dt dt 2 2
Problem 6
• A 3 kg mass has an initial velocity, v = (5i - 3j) m/s.• What is the kinetic energy at this time?• The velocity changes to (8i + 4j) 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.