A 6 m long plank of wood rests on a fulcrum 2 m from the left, as illus- trated in Fig 4.3.A boy of weight 500 N stands on the left edge of the plank, while a girl weighing 400 N stands 2 m from the right end.
(i) If the system is in equilibrium, calculate the weight of the metre stick. (ii) What is the reaction on the fulcrum?
(iii) If the boy was replaced by a man of weight 800 N standing on the same point, where would the girl need to position herself for the system to be in equilibrium again?
SAMPLE ANSWER 4C
(i) Using law 2:Taking the moments about the fulcrum (on the 2 m mark) Anticlockwise moments Clockwise moments (500)(2) W(1) (400)(2)
1 000 800 W The weight of the plank of wood is 200 N.
(ii) Using law 1: Forces up Forces Down R 500 200 400 The reaction at the fulcrum is 1 100 N.
(800)(2) 200(1) (400)(x) 1 600 200 400x
The girl is positioned 3.5 m to the right of the fulcrum, which is 50 cm from the right edge. x 1 400
400 3.5 EXERCISE 4.1 MOMENTS OF FORCES
Q1 What is the maximum torque that can be applied to a 20 cm long spanner by a 40 N force? Q2 A nut must be tightened to a torque of 30 N m.What size force is applied to a torque wrench of length 15 cm in order to provide this torque?
Q3 A chef applies 20 N of force in opposite directions on either side of the lid of a jar in order to open it. Calculate the turning effect of that couple if the diameter of the lid is 7 cm.
Q4 A 6 N m torque is provided by a pair of equal forces applied in opposite directions to the ends of the handlebars of a bicycle.The width of the handlebars is 50 cm.What is the size of the forces?
Q5 A metre stick is suspended at its centre of gravity along the 50 cm mark.A 6 N weight is hung from the 20 cm mark and another 6 N weight is hung from the 35 cm mark.Where must a third 6 N weight be hung from in order for the metre stick to be balanced?
66 INVESTIGATING PHYSICS 500
(iii) Using law 2:Taking the moments about the fulcrum (on the 2 m mark) Anticlockwise moments Clockwise moments
R 2 m 2 m 1 m W 400 Fig 4.4: Sample Answer 4C
Where: R is the reaction, W is the weight of the plank
