Homework 4
−
Solution
CHANG
1 The motion of the man is 1-D vertical motion downward. Since the platform
also travels downward along with the man, they move as one unit and we can take the man and
the platform together as the free body. Let the total mass for the man and the platform be
M
80
20
100 Kg, and the FBD is shown here:
Mg
T
T
T
+y
a
Note that the positive
y
−
axis is downward, same as the direction of the acceleration. Apply
Newton’s 2nd law:
F
y
ma
y
Mg
−
3
T
Ma
T
M
g
−
a
3
100
9.8
−
.2
3
320 N
From Newton’s 3rd law the force exerted by the man equals the tension in the cable, so
F
T
320 N.
CHANG
2 Since the marble settles at the same elevation on the inclined surface and rides
along with the spinning cone, its motion is a horizontal uniform circular motion. The FBD of
the marble is shown here:
w=mg
N
a
n
y
n
Set up
n
−
y
coordinate system with
n
axis pointing to the left toward the center of the
circular motion. Apply Newton’s 2nd law along both
y
and
n
axes, with
a
y
0 (motion is
horizontal) and radius
R
L
cos
from geometry:
F
y
ma
y
N
cos
−
mg
0
N
mg
cos
F
n
ma
n
N
sin
m
4
2
L
cos
T
2
L
gT
2
sin
4
2
cos
2
9.8
1.5
2
sin30
∘
4
2
cos
2
30
∘
0.372 m
Y&F
5.52 The motion of the rider on the giant swing is a horizontal uniform circular
motion, and the FBD of the rider (and the seat) is shown here:

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