Department of Mechanical Engineering
KNUST
ME 261 Dynamics of Solid Mechanics
Homework Due: Wednesday, May 04, 2022
1. The two blocks shown in Figure 1 are originally at rest. Neglecting the masses of the
pulleys and the effect of friction in the pulleys and between block A and the horizontal
surface, determine (a) the acceleration of each block, (b) the tension in the cable.
Figure 1
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2. Each flyball of the centrifugal governor shown in Figure 2 has a mass of 0.5 kg and
revolves at a constant speed v in the horizontal circle of 150-mm. radius shown.
Neglecting the weights of links AB, BC, AD, and DE, and sleeve CE, and requiring
that the links support only tensile forces, determine the range of the allowable values
of v so that the magnitudes of the forces in the links do not exceed 75 N
flyball
sleeve
Figure 2
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3. The jet aircraft shown in Figure 3 has total mass m = 20 000 kg and a centre of mass at
G. It has three engines with two of them at point C and the other one at D. At take-off,
each of the engines at C provides thrust T1= 2.4 kN and the engine at D provides thrust
T2=2.0 kN. The aircraft has three landing wheels: nose (front) wheel at A, and two wing
landing wheels at B. Assume that the normal reactions on the two wing landing wheels
are equal. In addition, neglect the mass of the wheels and any lift caused by the wings.
Using the dimensions d = 3 m, b= 2.5 m, c = 2.3 m, e =6 m, f = 1.2 m, determine (a)
the acceleration of the plane at take-off, (b) the normal reaction on the nose landing
wheel A, (c) the normal reaction on each wing landing wheel B.
D
T2
2T
b
G
C
c
f
A
B
d
e
Figure 3
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4. In Figure 4, the uniform pipe has a mass M=16000 kg and radius of gyration about the
z axis of kG=2.7 m. If the worker pushes on it with a horizontal force F=50 N, applied
perpendicular to the pipe, determine the pipe’s angular velocity when it has rotated
through angle θ=90o about the z axis, starting from rest. Assume the pipe does not
swing. Take r = 0.75 m and l = 3 m
Figure 4
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5. The punching bag shown in Figure 5 has mass m = 25 kg and radius of gyration about
its centre of mass G of kG=0.4 m. If it is subjected to a horizontal force F=150 N,
determine the initial angular acceleration of the bag and the tension in the supporting
cable AB. Take a=1.2 m, b = 0.3 m and c= 0.6 m.
Figure 5
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6. The compound pulley shown in Figure 6 has a mass of 60 kg and a radius of gyration
kO = 0.4 m. Two cords of negligible masses are wrapped around the peripheries of the
pulleys and attached to blocks A and B having a mass of mA= 30 kg and mB = 40 kg,
respectively. If the block is released, determine the drum's angular acceleration and
acceleration of each block. Take R1= 300 mm and R2= 500 mm.
R2
R1
O
A
B
Figure 6
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7. The double pulley brake drum shown in Figure 7 is used to control the motion of block
G of mass 50 kg. The inner and outer radii of the double pulley are R 1=200 mm and
R2= 250 mm, respectively. The double pulley has mass of 200 kg and radius of gyration
of 220 mm about the axis of rotation. The coefficient of kinetic friction between the
drum and brake pad C of lever ABC is 0.45. Block A is moving downward at speed of
10 m/s when the brake is suddenly applied to the drum by actuating the hydraulic
cylinder BF, and block G moves 1.4 m downward before coming to rest. Assume a
uniformly accelerated motion. Determine (a) the linear acceleration of the block and
the angular acceleration of the drum, (b) the time required for the cylinder to come to
rest, (c) the force induced by the hydraulic cylinder BF. Use Equation of Motion.
A
F
B
350 mm
400 mm
R2
250 mm
C
E
D
R1
G
50 kg
Figure 7
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8. Determine the time required for the for the cylinder in question 7 to come to rest using
the Impulse-Momentum method.
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