ENPH 131 Assignment #10
Solutions
Problem 15.79
The 3kg ball is thrown so that it travels horizontally at 10m/s when it strikes the 5kg block as it is traveling down the
inclined plane at 1m/s.
a) If the coefficient of restitution between the ball and the block is e = 0.4, determine the speed of the ball just after the
impact.
In the direction up the ramp:
Úm1 v1 = Úm2 v2
3 H10 cos 20 °L - 5 H1L = 3 vAx2 + 5 vBx2
1
vAx2 = 3 H23.191 - 5 vB2 L
e=
vBx2 -vAx2
vAx1 -vBx1
vBx2 -vAx2
10 cos 20 °+1
0.4 =
vBx2 = vAx2 + 4.159
vAx2 = 0.2996 m  s
vBx2 = 4.459 m  s
In the direction perpendicular to the ramp for ball A:
mA vAy1 = mA vAy2
vAy2 = -10 sin 20 ° = -3.420 m  s
vA2 = IvAx2 2 + vAy2 2 M
vA2 = 3.43 m  s
12
b) Determine the speed of the block just after the impact.
vB2 = 4.46 m  s
c) Also, what distance does B slide up the plane before it momentarily stops? The coefficient of kinetic friction between the
block and the plane is Μk = 0.4.
ÚFy = 0
-5 H9.81L cos 20 ° + N = 0
N = 46.092 N
2
ENPH 131 assignment 10 solutions.nb
ÚFy = 0
-5 H9.81L cos 20 ° + N = 0
N = 46.092 N
1
2
T1 + ÚU1-2 = T2
H5L H4.459L - 5 H9.81L sin 20 ° d - 0.4 H46.092L d = 0
d = 1.41 m
2
Problem 16.2
Just after the fan is turned on, the motor gives the blade an angular acceleration Α = I20 e-0.6 t M rad ‘ s2 , where t is in seconds.
a) Determine the speed of the tip P of one of the blades when t = 3s. When t = 0 the blade is at rest.
âw = Α ât
w
t
-0.6 t
Ù â w = Ù 20 e
0
ât
0
20
w = - 0.6 Ie-0.6 t - e0 M = 33.3 I1 - e-0.6 t M
At t = 3 s
w = 27.82 rad  s
vP = w r = 27.82 H1.75L
vP = 48.7 ft  s
b) How many revolutions has it made in the 3s?
âΘ = Ω ât
Θ
t
-0.6 t
Ù â Θ = Ù 33 I1 - e
0
M ât
0
1
Θ = 33.3 I3 + I 0.6 M Ie-0.6 t - 1MM
At 3s:
Θ = 53.63 rad =
53.63
2Π
rev = 8.54 rev
ENPH 131 assignment 10 solutions.nb
3
Problem 16.14
A disk having a radius of 7in. rotates about a fixed axis with an angular velocity of Ω = H2 t + 4L rad  s, where t is in seconds.
a) Determine the tangential component of acceleration of a point located on the rim of the disk at the instant the angular
displacement is Θ = 38 rad.
Α=
âΩ
ât
= 2 rad ‘ s2
7
at = Α rP = 2 I 12 M = 1.17 ft ‘ s2
b) Determine the normal component of acceleration of a point located on the rim of the disk at the instant the angular
displacement is Θ = 38 rad.
Ù âΘ = Ù Ω ât
Θ
t
Ù â Θ = Ù H2 t + 4L â t
0
0
Θ = t2 + 4 t
At Θ = 38 rad:
t2 + 4 t - 38 = 0
Positive root: t = 4.481s
Ω = 2 H4.481L + 4
Ω = 12.962 rad  s
7
an = Ω2 rP = I12.9622 M I 12 M = 98.0 ft ‘ s2
Problem 17.23
Determine the mass moment of inertia of the thin plate about an axis perpendicular to the page and passing through point O.
The material has a mass per unit area of 14 kg ‘ m2 .
Treat the system as two segments: A solid disk, and a square hole. The hole should be counted as a negetive part.
4
ENPH 131 assignment 10 solutions.nb
The masses of the segments are m1 = ΠI0.22 M H14L, m2 = H0.2L H0.2L H14L. Use the parallel-axis theorem:
IO = ÚIG + m d 2
1
1
IO = A 2 ΠI0.22 M H14L I0.22 M + ΠI0.22 M H14L I0.22 ME - A 12 H0.2L H0.2L H14L I0.22 + 0.22 M + H0.2L H0.2L H14L I0.22 ME
IO = 0.0794 kg × m2
Problem 17.40
The forklift and operator have a combined weight of 11000lb and center of mass at G.
a) If the forklift is used to lift the 2000lb concrete pipe, determine the normal reactions on each of its four wheels if the pipe
is given an upward acceleration of 3 ft ‘ s2 .
ÚMA = ÚHMk LA
2000
2000 H5L + 2 NB H10L - 11 000 H4L = -AI 32.2 M H4LE H5L
NB = 1640 lb
b)
ÚFy = mHaG Ly
2000
2 NA + 2 H1637.9L - 2000 - 11 000 = I 32.2 M H3L
NA = 4960 lb