Please include an appropriate free body diagram for each equation used. Also include a
sketch of the coordinates used in your equations.
Answers
:
v
A
2
=
6
m
/sec
v
B
2
=
16
m
/sec
Horizontal plane
A
B
v
B
36.87°
26
Problem 24
A homogeneous bar AB with a mass of M and length L is supported by cables AD and EG, where
G is the center of mass of the bar. At the position shown below, the bar is horizontal, point A is
directly below D, and end B is directly below E.
If the bar is released from rest in the position shown, determine the angular acceleration
of the bar
immediately after release. In your calculations, use M = 20 kg, L = 4 meters and h = 1.5 meters.
Ignore the mass of cables AD and EG.
You need to provide an accurate free body diagram of the bar and to indicate the coordinate
system used in order to receive full credit for this problem.
Answer:
"
=
2.58
rad
/sec
2
(
CW
)
A
G
B
D
E
g
L
h

27
Problem 25
Particle A, having a mass of m = 4 kg, initially moves to the left on a smooth horizontal
plane with a speed of
v
A
1
=
20
m
/sec
. Particle B, also having a mass of m = 4 kg, is
attached to an elastic cord whose unstretched length is 3 meters, whose stiffness is K =
100 newtons/meter and is attached to a fixed pin at O. Initially B is at rest at a distance of
R = 2 meters from O with
"
=
36.87
°
with the cord being slack. The impact of A with B
has a coefficient of restitution of e = 0.6.
a)
Draw a free body diagram (FBD) of A and B together during impact.
b)
Determine the speed of B immediately after being struck by A.
c)
Draw an FBD of B after impact.
d)
When the cord has stretched, such that B is at a distance of 5 meters from O, find
˙
R
and
˙
"
for the motion of B.
Answer to d):
˙
"
3
=
0.768
rad
/sec
˙
R
3
=
11.9
m
/sec
B
A
R
slack cord
O
v
A1
m
HORIZONTAL PLANE
m
!
28
Problem 26
A particle P having a mass of m = 10 kg is constrained to move in a horizontal plane. A
cable this attached to P is pulled over an ideal pulley with a constant force F = 800
newtons at the other end of the cable. The cable has a total length of L = 8 meters. When
d = 2 meters,
"
=
53.13
°
and P is moving to the left with a speed of
v
P
=
15
m
/sec
.
When d = 5 meters, find:
a) ˙ ". b) the speed of point A .
F
O
P
d
HORIZONTAL PLANE
v
P
!
A
R
e
R
e
!
Answer
:
v
A
2
=
11.4
m
/sec

29
Problem 27
Given
:
Particle A of mass m is moving in a horizontal plane
with initial velocity V
A1
,
with V
A1
being parallel to line BC. After impact with the
fixed
, rigid surface,
particle A rebounds with a velocity V
A2
, with V
A2
being parallel to line CD.
Line BC is perpendicular to line CD. Let e be the coefficient of restitution for
the impact of particle A with the surface. Consider the contacting surface to be
smooth.
Find
:
a) Determine the angle
%
needed to ensure that V
A2
is parallel to line CD.
Write your answer in terms of e only.
b) If e = 0.4, m = 3kg, and V
A1
= 5m/s, find the average force applied
to mass A during impact if the impact occurs over a period of
time of 0.002 sec.

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