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Dynamics 2e 807
Problem 4.100
The weights
B
in the pulley systems shown are identical and are
being lifted at the same constant speed
v
. Assume there are no
energy losses in the pulleys. Is the power developed by force
F1
in
(a) smaller than, equal to, or greater than that developed by force
F2
in (b)?
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.
808 Solutions Manual
Problem 4.101
For the two pulley systems shown, the block
B
has a mass
mBD
254 kg
and is being lifted with a constant speed
vD3m=s
. Deter-
mine the power developed by the forces F1and F2.
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 809
Problem 4.102
A truck crane with a mass of
40;000 kg
has an engine with a rated power
of
300 kW
. Assuming that all power is transmitted to the wheels and
that they do not slip, determine the maximum climb angle
✓
if the truck
is to maintain a constant speed of vtD25 km=h.
Solution
We model the truck as a particle subject to its own weight
mg
, the pro-
pelling force F, and the reaction Nnormal to the incline.
810 Solutions Manual
Problem 4.103
The
185 lb
man climbs a distance
hD13 ft
to the top of the ladder in
9
s. Determine his
average power output.
Solution
The average power is found by dividing the work done to lift the person over the distance
h
by the time taken
Dynamics 2e 811
Problem 4.104
A cyclist is riding with a speed
vD18 mph
over an inclined road with
✓D15ı
. Neglecting aerodynamic drag, if the cyclist were to keep his power
output constant, what speed would he attain if ✓were equal to 20ı?
Solution
We model the cyclist as a particle subject to its own weight
mg
, the propelling
force F, and the reaction Nnormal to the incline.
812 Solutions Manual
Problem 4.105
A
1500 kg
car is traveling up the slope shown at a constant speed.
Knowing that the maximum power output of the car is
160 hp
, at
what speed can the car travel if air resistance is negligible? Also,
knowing that
1
L of regular gasoline provides
34:8 MJ
of energy, how
many liters of gasoline will be required in
1
h if the engine has an
efficiency ✏D0:20?
Solution
We model the car as a particle subject to its own weight
mg
, the normal
reaction with the road N, and the propulsive force F.
Dynamics 2e 813
Problem 4.106
A
2600 lb
car on a straight horizontal road goes from
0
to
60 mph
in
7
s. Neglecting aerodynamic drag, if the force propelling the
car is constant during the acceleration phase, determine the power
developed by this force 7s after the beginning of the motion.
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.
814 Solutions Manual
Problem 4.107
The height
h
of the aerobic stepper shown is
25 cm
.A
65 kg
person goes up
and down the step once every
2
s. Accounting only for the work done in lifting
her body and assuming a muscle efficiency of
25
%, determine the calories
(1CD4:184 kJ) burned by the person in 1h.
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 815
Problem 4.108
The motor powering the pulley system shown is drawing
6kW
of power. The
crate
B
has a mass of
250 kg
. Determine the speed of the crate if the crate is
lifted at a constant speed and the motor’s efficiency is ✏D0:87.
Solution
We model the crate as a particle subject to its own weight
mg
and three times the tension in the
cord Fc.
816 Solutions Manual
Problem 4.109
The motor
B
is used to raise and lower the crate
C
by a pulley system. At the
instant shown, the cable is being retracted by the motor with the constant speed
vcD5ft=s. The weight of the crate is WCD450 lb.
If the power meter
A
shows a power input to the motor of
1:36 hp
, determine
the overall efficiency of the system.
Solution
