Worksheet I: Work and energy.
1. A 10.0kg crate is pulled 15.0 m up along a frictionless incline as shown in the figure
below. The crate starts at rest and has a final speed of 6.00 m/s.
a.
Draw the freebody diagram for the crate.
b.
Find the work done by the weight.
()
( )
2
10.0 kg
9.8 m/s
15 m sin 25
620 J
Wm
g
h
=−
°=−
(negative because weight points down and vertical displacement is up)
c.
Find the work done by the normal force exerted by the incline on the crate.
0 (the normal force is perpendicular to the displacement)
d.
Find the work done by the tension on the rope. You can do this both using the work
kinetic energy theorem or using Newton’s laws and the definition of work. You
should be able to do both.
WKE:
net
2
1
620 J
0
(10.0 kg) 6.0 m/s
0
2
800 J
gNT
T
T
WW
W
W
K
W
W
=++=
∆
−+
+
=
−
=
Newton’s laws:
( )
(
)
(
)
(
)
2
22
2
0
2
6.0 m/s
sin
with
1.2 m/s
1
5
m
sin
10.0 kg 1.2 9.8sin 25
m/s
53.4 N
53.4 N 15 m
800 J
T
vv
Tm
g
m
a
a
x
ag
WT
x
θ
−
−=
=
=
=
∆
=+
=
+
°
=
=∆=
=
motor
25
°
15 m
N
mg
T
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2.
A box of mass
M
= 1.5 kg is pushed against a horizontal spring of constant
k
=
1000 N/m. The spring is compressed a distance
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 Fall '08
 HerreraSiklody
 Energy, Force, Friction, Work, m/s

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