1. A drum containing 50litres of paint has a total mass of 70kg. The mass of the empty drum, including the lid, is 5kg.
(i) Calculate the relative density of the paint.
(ii) The drum is made of a metal of relative density 7.8. Calculate the volume of metal, in cm3 , used to make the drum and lid.
2. A belt is driven by a pulley. The tensions in the two parts of the belt are 60N and 80N, as shown in the diagram. Calculate the magnitude and direction of the total force exerted on the pulley by the belt.
3. A uniform springboard at a swimming pool has a weight of 150N and length 4.0m. It is held by two supports, A at one end and B, 1.5m from A.
(a) Calculate the force exerted by support A.
(b) A diver of mass 50kg walks to the end of the board. Calculate:
(i) the force exerted by support A.
(ii) the force exerted by support B.
4. The system of two weights hanging from a rope is in equilibrium with the rope in the centre exactly horizontal.
(a) By considering the equilibrium of point A, calculate tension T1, tension T2.
(b) By considering the equilibrium of point B, calculate angle θ and T3. 1
5. Calculate the x and y coordinates of the centroid of the area shown. Dimensions are in mm.
6. A steel wire of cross-sectional area 0.50mm2 and length 4.0m stretches elastically by 3.0mm when the tension in it is increased by 75N.
(i) the longitudinal stress applied to the wire.
(ii) the longitudinal strain produced.
(iii) the value of the Young modulus for this steel.
(b) The lift cable in a sky-scraper consists of 100 strands of this wire. By how much does a 90m length of this cable stretch when an 80kg passenger steps into the lift? The tension is the same in each cord.
7. A ball is thrown vertically upwards with an initial velocity of 25m/s from the base of a 15m cliff. Neglect air resistance and the small horizontal motion. Calculate:
(a) the height, h, by which the ball clears the top of the cliff,
(b) the time after release at which the ball lands at B,
(c) the impact velocity at B.
8. A footballer kicks a ball at 25m/s (with no spin) from the ground at 60° from the horizontal. (ignore air resistance)
(a) Calculate the time that the ball in the air.
(b) Calculate how far away from the footballer the ball hits the ground.
9. A trolley A (3kg) and mass B (2kg) are joined by a light inextensible string which passes over a smooth pulley fixed at the edge of a horizontal table. Initially, A is held at rest on the table while B hangs freely over the side.
(a) Calculate the acceleration which the system will have when mass A is released.
(b) Calculate the tension in the string.
10. Two smooth spheres A and B, of different mass, are travelling towards each other with speeds of 0.1m/s and 0.4m/s, as shown. After impact, the direction of both spheres is reversed and the speed of A is 0.2m/s. e = 0.6. Calculate
(i) the speed of B after the impact.
(ii) the ratio: (mass of A)/(mass of B).
11. A car of mass 1000kg, travelling at 100km/hr requires 60m to come to a halt in an emergency stop once the brakes are applied. The car decelerates at a constant rate because of the friction of its tyres on the road. Calculate the coefficient of friction.
12. A car, of mass 1000kg, travelling at 12ms−1 up a slope inclined at 15° to the horizontal, stops in a distance of 25m. Calculate the frictional force which must be acting.