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6.1 Work Done by a Constant Force
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Process of energy transfer: W = Fd cosθ
Scalar with units of Nm or J (Joule)
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6.1 Work Done by a Constant Force
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Work done by the … or work done on the ….
Positive work is done when
lifting the bag but no work is
done when walking with the
bag.
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6.3 Kinetic Energy
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Mechanical energy and the ability to do work.
Wnet = Fnetd = (ma)d
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From chapter 2: v22 = v12 + 2ad
Wnet = ½ mv22 – ½ mv12 = ΔKE
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6.3 Work – Energy Principle
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The work done by a net force will increase or
decrease the kinetic energy of an object.
Application of Newton’s 2nd and 3rd Laws of Motion
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6.4 Potential Energy
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Gravitational potential energy (PEgrav) depends on the
position of the object relative to its surroundings.
Wext = Fextd cos0° = mgh
WG = FGd cos180° = -mgh
PEgrav = mgy
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6.4 Potential Energy
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Springs follow Hooke’s Law: Fs = -kx
W = Fx = (½kx)x = ½kx2
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In class: Question 3 and Problem 3 (include a force diagram)
Other problems ↓
8. The piano is moving with a constant velocity down the plane.
(a) Write Newton’s 2nd law on each direction for the piano
FN
Ffr
y
FP
q
x
mg
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q
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F
F
y
 FN  mg cos q  0  FN  mg cos q
x
 mg sin q  FP  Ffr  0 
FP  mg sin q  Ffr  mg  sin q   k cos q 

  330 kg  9.80 m s 2


sin 28o  0.40 cos 28o  3.8  102 N
(b) The work done by the man is the work done by FP and the
angle between FP and direction of motion is 180°.
WP  FP d cos180o    380 N  3.6 m   1.4 103 J
o
W

F
d
cos180
   k mgd c
(c) the angle between Ffr and directionfr of motion
is 180°.
fr

Wfr  Ffr d cos180o    k mgd cos q  4.1
0.40
3330
 10
J kg  9.8 m
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 4.1 103 J
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(d) The angle between the force of gravity and the direction
of motion is 62o.
.



WGkgFG9.8
d cos
 mgd
33010
kg J 9.8 m s
2   330
m s62  3.6
m  cos 62  5.5
o
2 o
o
o
3
2
(e) Since the piano is not accelerated, the net force on the
piano is 0, and so the net work done on the piano is also 0. This
can also be seen by adding the three work amounts calculated.
WNet  WP  Wfr  WG  1400 J  4100 J  5500 J  0 J
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