kaplan (hmk378) – Homework 8 – Weathers – (17104)
1
This printout should have 12 questions.
Multiplechoice questions may continue on
the next column or page – fnd all choices
beFore answering.
001
(part 1 oF 2) 10.0 points
An amusement park ride consists oF a rotating
circular platForm 11 m in diameter From which
10 kg seats are suspended at the end oF 2
.
61 m
massless chains. When the system rotates,
the chains make an angle oF 14
.
7
◦
with the
vertical.
The acceleration oF gravity is 9
.
8 m
/
s
2
.
θ
l
d
What is the speed oF each seat?
Correct answer: 3
.
98035 m
/
s.
Explanation:
In the vertical direction we have
T
cos
θ
=
m g ,
where
T
is the tension in the chain. In the
horizontal direction we have
T
sin
θ
=
m v
2
r
.
Since
r
=
ℓ
sin
θ
+
d
2
= (2
.
61 m) sin 14
.
7
◦
+
11 m
2
= 6
.
16231 m
,
we have
v
=
r
g r
tan
θ
=
R
(9
.
8 m
/
s
2
) (6
.
16231 m) tan14
.
7
◦
= 3
.
98035 m
/
s
.
002
(part 2 oF 2) 10.0 points
IF a child oF mass 39
.
6 kg sits in a seat, what is
the tension in the chain (For the same angle)?
Correct answer: 502
.
529 N.
Explanation:
M
= 39
.
6 kg
±rom the frst part we have
T
cos
θ
= (
m
+
M
)
g
T
=
(
m
+
M
)
g
cos
θ
=
(10 kg + 39
.
6 kg) (9
.
8 m
/
s
2
)
cos 14
.
7
◦
= 502
.
529 N
.
003
10.0 points
A curve oF radius 59
.
9 m is banked so that
a car traveling with uniForm speed 65 km
/
hr
can round the curve without relying on Fric
tion to keep it From slipping to its leFt or right.
The acceleration oF gravity is 9
.
8 m
/
s
2
.
1
.
7 Mg
μ
≈
0
θ
What is
θ
?
Correct answer: 29
.
0457
◦
.
Explanation:
Let :
m
= 1700 kg
,
v
= 65 km
/
hr
,
r
= 59
.
9 m
,
and
μ
≈
0
.
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2
Basic Concepts:
Consider the free body
diagram for the car.
The forces acting on
the car are the normal force, the force due to
gravity, and possibly friction.
μ
N
N
cos
θ
m g
N
sin
θ
x
y
To keep an object moving in a circle re
quires a force directed toward the center of
the circle; the magnitude of the force is
F
c
=
m a
c
=
m
v
2
r
.
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 Fall '08
 Weathers
 mechanics, Force, Friction, Work, Correct Answer

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