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970 Solutions Manual
Problem 5.79
A golfer strikes a stationary ball
B
with a putter. At the time of impact, the
putter’s head
A
is traveling horizontally with a speed
v
AD1:2 m=s
. Model
the impact as an unconstrained direct central impact of two particles, and
let the masses of
A
and
B
be
mAD200
g and
mBD46
g, respectively.
Determine the COR of the collision if the postimpact speed of
B
is
vC
BD
1:76 m=s.
Solution
of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the
permission of McGraw-Hill, is prohibited.
Dynamics 2e 971
Problem 5.80
Car
A
, with
mAD1550 kg
, is stopped at a red light. Car
B
, with
mBD1865 kg
and a speed of
40 km=h
,
fails to stop before impacting car
A
. After impact, cars
A
and
B
slide over the pavement with a coefficient
of friction kD0:65.
How far will the cars slide if the cars become entangled?
Solution
Since
A
and
B
becomes entangled, we model their collision as a perfectly plastic
direct central impact of particles whose impact-relevant FBD is shown in the top
972 Solutions Manual
of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the
permission of McGraw-Hill, is prohibited.
Dynamics 2e 973
Problem 5.81
Car
A
, with
mAD1550 kg
, is stopped at a red light. Car
B
, with
mBD1865 kg
and a speed of
40 km=h
,
fails to stop before impacting car
A
. After impact, cars
A
and
B
slide over the pavement with a coefficient
of friction kD0:65.
How far will each car slide if the COR for the impact is eD0:2?
Solution
We divide the problem into two parts. First, we analyze the impact between
A
and
B
. Second we analyze the
motion of Aand Bafter the collision.
974 Solutions Manual
Sliding motion Aand Bafter impact.
Now we consider the postimpact motion of
A
and
B
. Referring to the figure at the right,
we model
A
and
B
as particles subject only to their respective weights
mAg
and
mBg
,
Dynamics 2e 975
Problem 5.82
A platform bench scale consists of a
120 lb
plate resting on linear
elastic springs whose combined spring constant is
kD5000 lb=ft
.
Let
WDk.ı ı0/
be the weight measurement actually provided by
the scale (that is, it reads zero pounds when nothing is on the plate),
where
ı0
is the spring’s compression due to the weight of the scale’s
plate.
A
50 lb
sack of portland cement is dropped (from rest) onto the
scale from a height
hD4ft
measured from the scale’s plate (there is
no rebound of the sack). Determine the maximum weight displayed
by the scale.
Solution
976 Solutions Manual
of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the
permission of McGraw-Hill, is prohibited.
Dynamics 2e 977
Problem 5.83
A platform bench scale consists of a
120 lb
plate resting on linear
elastic springs whose combined spring constant is
kD5000 lb=ft
.
Let
WDk.ı ı0/
be the weight measurement actually provided by
the scale (that is, it reads zero pounds when nothing is on the plate),
where
ı0
is the spring’s compression due to the weight of the scale’s
plate.
Repeat Prob. 5.82 with hD0ft.
Solution
If
h
were different from zero, we would have to solve the problem by first computing the speed with which
the cement sack strikes the scale’s plate. Then we would have to solve the impact problem associated to the
978 Solutions Manual
of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the
permission of McGraw-Hill, is prohibited.
Dynamics 2e 979
Problem 5.84
Bowling ball
A
, traveling with a speed
v
AD6ft=s
, arrives at a return station
and collides with ball
B
, which is in contact with ball
C
. Balls
B
and
C
are
initially at rest. Let
WADWBDWCD16 lb
be the weights of
A
,
B
, and
C
,
respectively. Determine the postimpact velocities of
A
,
B
, and
C
if the CORs
for all collisions are equal to 1.
Solution
