Addis Ababa University Addis Ababa Institute of Technology School Of Mechanical and Industrial Engineering Extension Division Assignment 2

Transcription

1 Addis Ababa University Addis Ababa Institute of Technology School Of Mechanical and Industrial Engineering Extension Division Assignment 2 1. The 50-kg crate is projected along the floor with an initial speed of 7 m/s at x=0. The coefficient of kinetic friction is Calculate the time required for the crate to come to rest and the corresponding distance x traveled. 2. Determine the initial acceleration of the 15-kg block if (a) T=23N and (b) T=26 N. The system is initially at rest with no slack in the cable, and the mass and friction of the pulleys are negligible. 3. The small 0.6-kg block slides with a small amount of friction on the circular path of radius 3 m in the vertical plane. If the speed of the block is 5 m/s as it passes point A and 4 m/s as it passes point B, determine the normal force exerted on the block by the surface at each of these two locations. 4. At the instant when θ =30 o, the horizontal guide is given a constant upward velocity v o = 2m/s. For this instant calculate the force N exerted by the fixed circular slot and the

2 force P exerted by the horizontal slot on the 0.5-kg pin A. The width of the slots is slightly greater than the diameter of the pin, and friction is negligible. 5. The spring is unstretched when x=0. If the body moves from the initial position x 1 =100mm to the final position x 2 =200mm, (a) determine the work done by the spring on the body and (b) determine the work done on the body by its weight. 6. The 2-kg collar is released from rest at A and slides down the inclined fixed rod in the vertical plane. The coefficient of kinetic friction is Calculate (a) the velocity v of the collar as it strikes the spring and (b) the maximum deflection x of the spring. 7. The 6kg cylindrical collar is released from rest in the position shown and drops onto the spring. Calculate the velocity v of the cylinder when the spring has been compressed 50mm.

3 8. The 4-kg slider is released from rest at A and slides with negligible friction down the circular rod in the vertical plane. Determine (a) the velocity v of the slider as it reaches the bottom at B and (b) the maximum deformation x of the spring. 9. The two 1.5-kg spheres are released from rest and gently nudged outward from the position θ =0 and then rotate in a vertical plane about the fixed centers of their attached gears, thus maintaining the same angle for both rods. Determine the velocity v of each sphere as the rods pass the position θ =30 o. The spring is unstretched when θ =0, and the masses of the two identical rods and the two gear wheels may be neglected. 10. A 0.2-kg particle is moving with a velocity v1 = i+ j+ 2k m/s at time t 1 =1s.If the single 2 force F= (5 + 3 ti ) + (2 t) j+ 3kN acts on the particle, determine its velocity v 2 at time t 2 = 4 s. 11. A 60-g bullet is fired horizontally with a velocity v 1 =600m/s into the 3-kg block of soft wood initially at rest on the horizontal surface. The bullet emerges from the block with the velocity v 2 =400m/s, and the block is observed to slide a distance of 2.70 m before coming to rest. Determine the coefficient of kinetic friction µ k between the block and the supporting surface. 12. The cart is moving down the incline with a velocity v 0 = 20 m/s at t= 0, at which time the force P begins to act as shown. After 5 seconds the force continues at the 50-N level.

4 Determine the velocity of the cart at time t= 8 s and calculate the time t at which the cart velocity is zero. 13. The 3-kg sphere moves in the x-y plane and has the indicated velocity at a particular instant. Determine its (a) linear momentum, (b) angular momentum about point O, and (c) kinetic energy A particle with a mass of 4 kg has a position vector in meters given by r = 3t i 2tj 3tk, where t is the time in seconds. For t = 3s determine the magnitude of the angular momentum of the particle and the magnitude of the moment of all forces on the particle, both about the origin of coordinates. 15. A particle of mass m is released from rest in position A and then slides down the smooth vertical plane track. Determine its angular momentum about both points A and D (a) as it passes position B and (b) as it passes position C. 16. The two bodies have the masses and initial velocities shown in the figure. The coefficient of restitution for the collision is e =0.3, and friction is negligible. If the time duration of

5 the collision is s, determine the average impact force which is exerted on the 3-kg body. 17. The sphere of mass m 1 travels with an initial velocity v 1 directed as shown and strikes the sphere of mass m 2. For a given coefficient of restitution e, determine the mass ratio m 1 /m 2 which results in m 1 being motionless after the impact. 18. Determine the value of the coefficient of restitution e for which the outgoing angle is one-half of the incoming angle as shown. Evaluate your general expression for θ =40 o.