PROBLEM 13.167
Two identical hockey pucks are moving on a hockey rink at the same speed of
3 m/s and in perpendicular directions when they strike each other as shown.
Assuming a coefficient of restitution e = 0.9, determine the magnitude and direction
of the velocity of each puck after impact.
SOLUTION
PROBLEM 13.167 (Continued)
PROBLEM 13.168
The coefficient of restitution is 0.9 between the two 60–mm–
diameter billiard balls A and B. Ball A is moving in the
direction shown with a velocity of 1 m/s when it strikes ball B,
which is at rest. Knowing that after impact B is moving in the x
direction, determine (a) the angle
,
θ
(b) the velocity of B after
impact.
BB
PROBLEM 13.169
A boy located at Point A halfway between the center O of a
semicircular wall and the wall itself throws a ball at the wall in a
direction forming an angle of
45°
with OA. Knowing that after
hitting the wall the ball rebounds in a direction parallel to OA,
determine the coefficient of restitution between the ball and the
wall.
SOLUTION
PROBLEM 13.170
The Mars Pathfinder spacecraft used large airbags to cushion
its impact with the planet’s surface when landing. Assuming
the spacecraft had an impact velocity of 18 m/s at an angle of
45° with respect to the horizontal, the coefficient of restitution
is 0.85 and neglecting friction, determine (a) the height of the
first bounce, (b) the length of the first bounce. (Acceleration of
gravity on the Mars = 3.73 m/s2.)
SOLUTION
PROBLEM 13.170 (Continued)
PROBLEM 13.171
A girl throws a ball at an inclined wall from a height of 3
ft, hitting the wall at A with a horizontal velocity
0
v
of
magnitude 25 ft/s. Knowing that the coefficient of
restitution between the ball and the wall is 0.9 and
neglecting friction, determine the distance d from the
foot of the wall to the Point B where the ball will hit the
ground after bouncing off the wall.
00
22
y
PROBLEM 13.171 (Continued)
2
PROBLEM 13.172
Rockfalls can cause major damage to roads and infrastructure. To design
mitigation bridges and barriers, engineers use the coefficient of restitution
to model the behavior of the rocks. The rock A falls a distance of 20 m
before striking an incline with slope α = 40o. Knowing that the coefficient
of restitution between A and the incline is 0.2, determine the velocity of
the rock after the impact.
SOLUTION
B
PROBLEM 13.173
From experimental tests, smaller boulders tend to have a greater
coefficient of restitution than larger boulders. The rock A falls a distance
of 20 meters before striking an incline with slope α = 45o. Knowing that
h= 30 m and d= 20 m, determine if a boulder will land on the road or
beyond the road for a coefficient of restitution of (a) e= 0.2, (b) e= 0.1.
PROBLEM 13.173 (Continued)
2
1
PROBLEM 13.174
Two cars of the same mass run
head–on into each other at C. After
the collision, the cars skid with
their brakes locked and come to a
stop in the positions shown in the
lower part of the figure. Knowing
that the speed of car A just before
impact was 5 mi/h and that the
coefficient of kinetic friction
between the pavement and the tires
of both cars is 0.30, determine
(a) the speed of car B just before
impact, (b) the effective coefficient
of restitution between the two cars.
PROBLEM 13.174 (Continued)
(37.53)
−
PROBLEM 13.175
A 1–kg block B is moving with a velocity v0 of magnitude
0
2 m/sv=
as
it hits the 0.5–kg sphere A, which is at rest and hanging from a cord
attached at O. Knowing that
0.6
k
m
=
between the block and the
horizontal surface and
0.8e=
between the block and the sphere,
determine after impact (a) the maximum height h reached by the sphere,
(b) the distance x traveled by the block.
SOLUTION
PROBLEM 13.175 (Continued)
PROBLEM 13.176
A 0.25-lb ball thrown with a horizontal velocity v0 strikes a 1.5–lb plate attached to a vertical wall at a height
of 36 in. above the ground. It is observed that after rebounding, the ball hits the ground at a distance of 24 in.
from the wall when the plate is rigidly attached to the wall (Figure 1) and at a distance of 10 in. when a foam–
rubber mat is placed between the plate and the wall (Figure 2). Determine (a) the coefficient of restitution
e between the ball and the plate, (b) the initial velocity v0 of the ball.
SOLUTION
02
BP
g gg
PROBLEM 13.176 (Continued)
0 2 02
0.25 0.25( ) 1.5 ( ) 6
B p Bp
v v vv v v
′ ′ ′′
=− + ⇒=− −
(3)
Solving (2) and (3) for
2
( ),
B
v′
20
(6 1)
() 7
B
e
vv
−
′=
Projectile motion
0
(6 1)
0.8333 7
evt
−
=
(4)
Dividing Equation (4) by Equation (1)
0.8333 6 1; 2.91655 6 1
27
eee
e
−
= = −
0.324e=
(b) From Figure (1)
Projectile motion,
22
11
; 3 (32.2)
22
h gt t= =
2
6 32.2t=
(5)
From Equation (1),
014.30 ft/sv=
PROBLEM 13.177
After having been pushed by an airline employee, an empty
40–kg luggage carrier A hits with a velocity of 5 m/s an
identical carrier B containing a 15–kg suitcase equipped with
rollers. The impact causes the suitcase to roll into the left wall
of carrier B. Knowing that the coefficient of restitution between
the two carriers is 0.80 and that the coefficient of restitution
between the suitcase and the wall of carrier B is 0.30, determine
(a) the velocity of carrier B after the suitcase hits its wall for
the first time, (b) the total energy lost in that impact.
SOLUTION
CB
PROBLEM 13.177 (Continued)
PROBLEM 13.178
Blocks A and B each weigh 0.8 lb
and block C weighs 2.4 lb. The
coefficient of friction between the
blocks and the plane is
0.30.
k
m
=
Initially block A is moving at a
speed
0
15 ft/sv=
and blocks B and
C are at rest (Fig. 1). After A
strikes B and B strikes C, all three
blocks come to a stop in the
positions shown (Fig. 2).
Determine (a) the coefficients of
restitution between A and B and
between B and C, (b
) the
displacement x of block C.
SOLUTION