Homework 8

Homework 8
ME 121: Engineering Mechanics II
D. H. Kelley
55 points
1. The concrete shape shown in Fig. 1 is formed by rotating the shaded area about the y axis. Determine
the moment of inertia Iy . The specific weight of concrete is γ = 150 lb/ft3 . (6 points)
Figure 1: Problem 1.
Figure 2: Problem 2.
2. The mountain bike shown in Fig. 2 has a mass of 40 kg with center of mass at point G1 , whereas the
rider has a mass of 60 kg with center of mass at point G2 . Determine the maximum deceleration when
the brake is applied to the front wheel, without causing the rear wheel B to leave the ground. Assume
the front wheel does not slip. Neglect the mass of all the wheels. (6 points)
3. The pipe shown in Fig. 3 has a mass of 800 kg and is being towed behind a truck. If the angle θ = 30◦ ,
determine the acceleration of the truck and the tension in the cable. The coefficient of kinetic friction
between the pipe and the ground is µk = 0.1. (7 points)
Figure 3: Problem 3.
Figure 4: Problem 4.
4. If shaft BC, shown in Fig. 4, is subjected to a torque M = (0.45t1/2 ) N · m, where t is in seconds,
determine the angular velocity of the 3-kg rod AB when t = 4 s, starting from rest. Neglect the mass
of shaft BC. (8 points)
5. The 15-kg block A and 20-kg cylinder B, shown in Fig. 5, are connected by a light cord that passes
over a 5-kg pulley (disk). If the system is released from rest, determine the cylinder’s velocity after its
has traveled downwards 2 m. The coefficient of kinetic friction between the block and the horizontal
plane is µk = 0.3.Assume the cord does not slip over the pulley. (10 points)
6. The uniform rod having a weight 10 lb is pin supported at A from a roller which rides on a horizontal
track, as shown in Fig. 6. If the rod is originally at rest, and a horizontal force F = 15 lb is applied to
the roller, determine the acceleration of the roller. Neglect the mass of the roller and its size d in the
computations. (9 points)
Figure 6: Problem 6.
Figure 5: Problem 5.
7. The uniform beam shown in Fig. 7 has a weight W . If it is originally at rest while being supported at
A and B by cables, determine the tension in cable A if cable B suddenly fails. Assume the beam is a
slender rod. (9 points)
Figure 7: Problem 7.