Homework 5 ME 121: Engineering Mechanics II D. H. Kelley 55 points 1. For a short period of time, the frictional driving force acting on the wheels of a 2.5-Mg van is FD = (600t2 ) N, where t is in seconds. If the van has a speed of 20 km/h when t = 0, determine its speed when t = 5 s. (6 points) 2. A particle is acted upon by three forces, described in Cartesian coordinates: F1 = {5i + 2tj + tk} lb, F2 = {t2 i} lb, and F3 = {−3k} lb (its weight). At t = 0, the particle has velocity v1 = {3i + 1j + 6k} ft/s. Determine its speed after 2 s. (6 points) 3. The 50-kg boy shown in Fig. 1 jumps onto the 5-kg skateboard with a horizontal velocity of 5 m/s. Determine the distance s the boy reaches up the inclined plane before momentarily coming to rest. Neglect the skateboard’s rolling resistance. (8 points) Figure 1: Problem 3. Figure 2: Problem 4. 4. The 5-kg block shown in Fig. 2 is falling downward with speed v1 = 2 m/s when it is 8 m from the sandy surface. Determine the average impulsive force acting on the block by the sand if the motion of the block is stopped in 0.9 s once the block strikes the sand. Neglect the distance the block dents into the sand and assume the block does not rebound. Neglect the weight of the block during impact with the sand. (6 points) 5. The free-rolling ramp shown in Fig. 3 has a mass of 40 kg. A 10-kg crate is released from rest at A and slides down 3.5 m to point B. If the surface of the ramp is smooth, determine the ramp’s speed when the crate reaches B. Also, what is the velocity of the crate? (9 points) Figure 3: Problem 5. Figure 4: Problem 7. 6. A ball of mass m is dropped vertically from a height h0 above the ground. If it rebounds to a height h1 , determine the coefficient of restitution between the ball and the ground. (7 points) 7. Two smooth disks A and B, shown in Fig. 4, each have a mass 0.5 kg. If both disks are moving with the velocities shown when they collide, determine the coefficient of restitution between the disks if after the collision B travels along a line 30◦ counterclockwise from the y axis. (8 points) 8. A ball is thrown onto a rough floor at an angle θ, as shown in Fig. 5. If it rebounds at an angle φ and the coefficient of kinetic friction is µ, determine the coefficient of restitution e. Neglect the size of the ball. Hint: Show that during impact, the average impulses in the x and y directions are related by Ix = µIy . Since the time of impact is the same, Fx ∆t = µFy ∆t and therefore Fx = µFy . (8 points) Figure 5: Problem 8. 2

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