6. (a) Define the moment of a force. A toy, such as that shown, has a heavy hemispherical base and its centre of gravity is located at C. When the toy is knocked over, it always returns to the upright position. Explain why this happens.
(12)
(b) State the conditions necessary for the equilibrium of a body under a set of co-planar forces.
(9)
Three children position themselves on a uniform see-saw so that it is horizontal and in equilibrium. The fulcrum of the see-saw is at its centre of gravity. A child of mass 30 kg sits 1.8 m to the left of the fulcrum and another child of mass 40 kg sits 0.8 m to the right of the fulcrum.
Where should the third child of mass 45 kg sit, in order to balance the see-saw?
2008
12. (a) In a pole–vaulting competition an athlete, whose centre of gravity is 1.1 m above the ground, sprints from rest and reaches a maximum velocity of 9.2 m s–1 after 3.0 seconds. He maintains this velocity for 2.0 seconds before jumping.
Draw a velocity–time graph to illustrate the athlete’s horizontal motion.
Use your graph to calculate the distance travelled by the athlete before jumping.
2007 6. State Hooke’s law.
Calculate its spring constant.
The sphere is pulled down until the length of the spring is 310 mm. The sphere is then released and oscillates about a fixed point.
Derive the relationship between the acceleration of the sphere and its displacement from the fixed point. Why does the sphere oscillate with simple harmonic motion?
Calculate: (i) the period of oscillation of the sphere (ii) the maximum acceleration of the sphere
(iii) the length of the spring when the acceleration of the sphere is zero.
(acceleration due to gravity = 9.8 m s–2) (23) (18) (6)
A stretched spring obeys Hooke’s law. When a small sphere of mass 300 g is attached to a spring of length 200 mm, its length increases to 285 mm.
