Answer Happy

Question 1 (a) Figure Q1a shows two particles of mass 4 kg and 2 kg that are connected by a light string passing over a smooth fixed pulley. The particles hang freely and are released from rest. Find 1. the acceleration a m/s of the two particles, (3 marks) II. the tension, TN, in the string, and (3 marks) III. State any assumptions made (2 marks) a 4 kg 2 kg Figure Qla (b) I. A cyclist rides along a straight road from a point A to a point B. She starts from rest at A and accelerates uniformly to reach a speed of 12 m/s in 8.3 seconds. She maintains this speed for a further 20.7 seconds and then uniformly comes to rest at B. The whole journey takes 35.8 seconds. draw a velocity-time graph for the motion (3 marks) From your graph find: II. her acceleration for the first part of the motion (2 marks) her retardation for the last part of the motion (2 marks) the total distance travelled (3 marks) describe the geometric relationship between your answer in (iii) and your graph? III. IV. V.
Question 2 (a) Two smooth spheres A and B of masses 150 grams and 350 grams are travelling towards reach other along the same horizontal line with speeds of 4 m/s and 2 m/s respectively. After the collision, the direction of motion of Bis reversed and it is travelling at a speed of 1 m/s. Find 1. the speed of A after the collision, (4 marks) II. the loss of kinetic energy due to the collision, and (4 marks) III. determine the coefficient of restitution between the two bodies and comment on your result. (2 marks) (b) A block of mass 102.5 kg rests on a rough inclined plane with a coefficient of friction of 0.3. The plane makes an angle of with the horizontal as shown in Figure 02b. 102.5 kg Figure Q2b I. draw the free body diagram (1 mark) II. determine the maximum value of that will cause the block to slide down the plane (3 marks) If the angle 8 = 25° and a force F is applied to push the block up the plane and it moves with a constant acceleration of 0.5 m/s. III. draw the free body diagram, and (2 marks) calculate the value of the force F. (4 marks) IV.
Question 3 (a) Figure Q3a shows a cantilever beam which is acted on by three forces as shown. The beam is in static equilibrium 1. draw the free body diagram of the beam, and (2 marks) II. determine the reaction force and moment at point P. (8 marks) 150 N 400 N 42° 65° P 2.5 m 3.6 m 7.5 m 30° Figure Q3a 250 N (b) A mass of 8 kg attached at the end of spring causes it to deflect by 35 mm. Determine 1. the spring stiffness (2 marks) II. the natural frequency of vibration (3 marks) III. the maximum velocity and acceleration of the mass if the amplitude of vibration is 35mm. (5 marks)
- The following equations may be used without proof. Angular motion: 8 = extar 0},=+of -?200 To calculate the moment of inertia l of a body: I = mk, where k is the radius of gyration. Linear motion: v=w+at or v-urat Sul (v2-1) 2a or - = 2as Simple Harmonic Motion: Sine/cosine wave: x = Asino, * = 4,cos, -4 sine, a=2. x= Acose). *=-dessin e), 1 I=-decos, 2 Kinetics: Newton's 2 Law F=ma In rotational form: T =la or T = 10 Skid and overturn equations for a car of track 2d: Skid: vurg Overturn: v red Energy Change in kinetic energy: KE = m*: Change in potential energy: PE = mg When a body of mass m is travelling at constant velocity v: Power = Fv Impacting bodies Conservation of momentum: (m )=E(mv) Coefficient of restitution: e