14–41.
SOLUTION
+b©Fn=man;2sin 45° =2
32.2 av2
1.5 b
A 2-lb block rests on the smooth semicylindrical surface.An
elastic cord having a stiffness is attached to the
block at Band to the base of the semicylinder at point C.If
the block is released from rest at A (), determine the
unstretched length of the cord so that the block begins to
leave the semicylinder at the instant . Neglect the
size of the block.
u=45°
u=0°
k=2lb>ft
CA
u
B
k2lb/ft
1.5 ft
Ans:
418
14–42.
The jeep has a weight of 2500 lb and an engine which
transmits a power of 100 hp to all the wheels.Assuming the
wheels do not slip on the ground, determine the angle of
the largest incline the jeep can climb at a constant speed
v=30 ft>s.
u
SOLUTION
θ
Ans:
419
14–43.
SOLUTION
Power: The power output can be obtained using Eq. 14–10.
Determine the power input for a motor necessary to lift
300
lb
at a constant rate of The efficiency of the motor is
.P=0.65
5ft
>
s.
Ans:
420
*14–44.
SOLUTION
Equation of Motion: The force Fwhich is required to maintain the car’s constant
speed up the slope must be determined first.
Power: Here, the speed of the car is .
y=
B
100(103)m
h
R
*a1h
3600 s b=27.78 m>s
An automobile having a mass of 2 Mg travels up a 7° slope
ataconstant speed of If mechanical friction
and wind resistance are neglected, determine the power
developed by the engine if the automobile has an efficiency
P=0.65.
v=100 km>h.
7
Ans:
421
14–45.
SOLUTION
At .
600 ms>h
h
ilki
i
b
j
i
h
is placed in a plane having a weight of 13000 lb. If the engine
develops a constant thrust of 5200 lb, determine the power
output of the plane when it is just ready to take off with a
speed of 600 mi>h.
Ans:
14–46.
SOLUTION
car having aweight of 5000 lb that is traveling at .If
the car is brought to astop,determine how long a100-W light
bulb must burn to expend the same amount of energy.
11mi=5280 ft.2
35 mi>h
Ans:
423
14–47.
SOLUTION
Step height: 0.125 m
The number of steps: 4
0.125 =32
15 ft
The escalator steps move with a constant speed of 0.6 m
>
s.
If the steps are 125 mm high and 250 mm in length,
determine the power of a motor needed to lift an average
mass of 150 kg per step. There are 32 steps.
Ans:
424
*14–48.
SOLUTION
Power: The work done by the man is
Thus, the power generated by the man is given by
The man having the weight of 150 lb is able to run up
a 15-ft-high fl ight of stairs in 4 s. Determine the power
generated. How long would a 100-W light bulb have to burn
to expend the same amount of energy? Conclusion: Please
turn off the lights when they are not in use! 15 ft
Ans:
425
14–49.
SOLUTION
Kinematics:The constant acceleration of the car can be determined from
Power: The maximum power output of the motor can be determined from
Thus, the maximum power input is given by
The average power output can be determined from
The 2-Mg car increases its speed uniformly from rest to
in 30 s up the inclined road. Determine the
maximum power that must be supplied by the engine, which
operates with an efficiency of . Also, find the
average power supplied by the engine.
P=0.8
25 m>s
10
1
Ans:
426
14–50.
SOLUTION
2sP+sM=l
Determine the power output of the draw-works motor M
necessary to lift the 600-lb drill pipe upward with a constant
speed of The cable is tied to the top of the oil rig,
wraps around the lower pulley, then around the top pulley,
and then to the motor.
4ft>s.
M
Ans:
14–51.
The 1000-lb elevator is hoisted by the pulley system and
motor M. If the motor exerts a constant force of 500 lb on
the cable, determine the power that must be supplied to the
motor at the instant the load has been hoisted
s=15 ft
starting from rest. The motor has an efficiency of
e=0.65.
SOLUTION
Equation of Motion. Referring to the FBD of the elevator, Fig. a,
Power. Applying Eq. 14–9, the power output is
The power input can be determined using Eq. 14–9
M
Ans:
*14–52.
The 50-lb crate is given a speed of 10 ft
>
s in
t=4 s
starting
from rest. If the acceleration is constant, determine the
power that must be supplied to the motor when
t=2 s.
The motor has an efficiency
e=0.65.
Neglect the mass of
the pulley and cable.
SOLUTION
M
Ans:
14–53.
The sports car has a mass of 2.3 Mg,and while it is traveling
at 28 m/sthe driver causes it to accelerate at If the
drag resistance on the car due to the wind is
where vis the velocity in m/s, determine the power supplied
to the engine at this instant. The engine has a running
efficiency of P=0.68.
FD=10.3v22N,
5m>s2.
SOLUTION
:
+©Fx=ma
x;F–0.3v2=2.3(103)(5)
F
D
430
14–54.
SOLUTION
starting from rest. If the drag resistance on the car
due to the wind is where vis the velocity in
m/s, determine the power supplied to the engine when
The engine has a running efficiency of P=0.68.t=5s.
FD=110v2N,
6m>s2,
D
431
14–55.
SOLUTION
Elevator:
Since ,
a=0
Hoisting is provided by the motor Mand the 60-kg block C.
If the motor has an efficiencyofdetermine the
power that must be supplied to the motor when the elevator
is hoisted upward at aconstant speed of vE=4m>s.
P=0.6,
E
C
M
v
E
Ans:
432
*14–56.
SOLUTION
Work of F
U1–2=25(5 –3.464) =38.40 lb #ft
applying a constant vertical force of to the cord.
If the rod is smooth, determine the power developed by the
force at the instant u=60°.
F=25 lb
4ft
A
3ft
F
u
Ans:
14–57.
SOLUTION
T
h
e 10-
lb
co
ll
ar starts from rest at Aan
d
i
s
li
fte
d
w
i
t
h
a
constant speed of along the smooth rod. Determine the
power developed by the force Fat the instant shown.
2ft>s
4ft
A
3ft
F
u
Ans:
434
14–58.
SOLUTION
When s=1.5 ft,
The 50-lb block rests on the rough surface for which
the coeffi cient of kinetic friction is mk=0.2. A force
F=
(
40 +s2
)
lb, where s is in ft, acts on the block in the
direction shown. If the spring is originally unstretched
(s=0) and the block is at rest, determine the power
developed by the force the instant the block has moved
s=1.5 ft.
F
k = 20 lb ft
30°
Ans:
435
14–59.
SOLUTION
Step height: 0.125 m
The escalator steps move with a constant speed of
If the steps are 125 mm high and 250 mm in length,
determine the power of a motor needed to lift an average
mass of 150 kg per step.There are 32 steps.
0.6 m
>
s.
4 m
125 mm
250 mm
v0.6 m/s
Ans:
*14–60.
SOLUTION
125 mm
250 mm
v0.6 m/s
If the escalator in Prob. 14–47 is not moving, determine the
constant speed at which a man having a mass of 80 kg must
walk up the steps to generate 100 W of power—the same
amount that is needed to power a standard light bulb.
Ans: