Patel (pnp223) – homework 16 – Turner – (92160)
1
This printout should have 12 questions.
Multiplechoice questions may continue on
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beFore answering.
001
10.0 points
Suppose you want to ride your mountain bike
up a steep hill. Two paths lead From the base
to the top, one twice as long as the other.
Compared to the average Force you would
exert iF you took the short path, the average
Force you exert along the longer path is
1.
Four times as small
2.
halF as small
correct
3.
the same
4.
three times as small
5.
undeterminedit depends on the time
taken
Explanation:
The gravitational potential energy gained
is the same in both cases and is equal to
the average Force exerted times the distance
traveled.
002
(part 1 oF 6) 10.0 points
A heavy ball swings on a string in a circular
arc oF radius 1 m.
Q
1 m
Q
′
P
35
◦
The two highest points oF the ball’s trajec
tory are
Q
and
Q
′
; at these points the string is
±
35
◦
From the vertical. Point
P
is the lowest
point oF the ball’s trajectory where the string
hangs vertically down.
The acceleration oF gravity is 9
.
8 m
/
s
2
.
What is the ball’s speed at the point
P
? Ne
glect air resistance and other Frictional Forces.
Correct answer: 1
.
88272 m
/
s.
Explanation:
Let :
g
= 9
.
8 m
/
s
2
,
m
= 3 kg
,
ℓ
= 1 m
,
and
θ
= 35
◦
.
The diagram For the velocity and accelera
tion oF the ball at point
P
is as Follows,
x
y
v
a
The di±erence oF gravitational potential en
ergy oF the ball between point
Q
and point
P
is Δ
U
=
U
Q
−
U
P
=
mg ℓ
(1
−
cos
θ
). The
velocity oF the ball at point
Q
is zero, so
K
P
+
U
P
=
K
Q
+
U
Q
K
P
+
U
P
= 0 +
U
Q
.
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 Spring '09
 Turner
 Physics, Kinetic Energy, Potential Energy, Work, Velocity, patel

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