2

Hong Kong Polytechnic University Department of Mechanical Engineering ME31003, Assignment 2

Due Time: Before 5:00PM, 2nd Mar. 2018 Notes: • • •

Please hand in hardcopy of your solution. 30 marks will be deducted for the late submission before the answer is posted on blackboard website. 80 marks will be deducted for the late submission after the answer is posted on blackboard website.

Name: ___________________

Student Number: ____________________

1) A 1.4kg model rocket is launched vertically from rest with a constant thrust of 25N until the rocket

reaches an altitude of 15m and the thrust ends. Neglecting air resistance, determine (a) the speed of the rocket when the thrust ends. (b) the maximum height reached by the rocket. (c) the speed of the rocket when it returns to the ground.

(7 marks) (7 marks) (7 marks)

2) A 2-kg collar is attached to a spring and slides without friction in a vertical plane along the curved

rod ABC. The spring is undeformed when the collar is at C and its constant is 600N/m. If the collar is released at A with no initial velocity, determine its velocity (a) as it passes through B. (10 marks) (b) as it reaches C. (10 marks)

3) The coefficient of restitution between the two collars is known to be 0.70. Determine

(a) their velocities after impact. (b) the energy loss during impact.

(10 marks) (9 marks)

1

4) A 1-kg block B is moving with a velocity v0 of magnitude v0 = 2 m/s as it hits the 0.5-kg sphere A,

which is at rest and hanging from a cord attached at O. Knowing that μk = 0.6 between the block and the horizontal surface and e = 0.8 between the block and the sphere, determine after impact (a) the maximum height h reached by the sphere. (12 marks) (b) the distance x traveled by the block. (8 marks)

5) A 2-kg block A is pushed up against a spring compressing it a distance x. The block is then released

from rest and slides down the 20º incline until it strikes a 1-kg sphere B, which is suspended from a 1-m inextensible rope. The spring constant k = 800 N/m, the coefficient of friction between A and the ground is 0.2, the distance A slides from the unstretched length of the spring d = 1.5 m and the coefficient of restitution between A and B is 0.8. Knowing the tension in the rope is 20 N when a = 40o, determine initial compression x of the spring (20 marks)

2