A non-uniform plank weighing 300N is set up as shown. The spring balance reads 160 N when the small boy stands at A, and 760 N when the small boy stands at B.
a) State what is meant by moment of a force.
b) Calculate the weight of the boy.
Answer:
a) The moment of a force is the turning effect of the force. It is calculated by the multiplication of the force and the perpendicular distance from the pivot.
b)
Let the weight of the boy be W.
Let the distance from the pivot to the c.g. of the plank be x.
When the boy is at A, taking pivot about pivot point (so that R can be ignored)
Clockwise moments = 300x
Anti-clockwise moments = 160 * 5 + 2W
At equilibrium, clockwise moments = anti-clockwise moments
300x = 800 + 2W --------------------------- (1)
Note: R is ignored because the perpendicular distance between R and the pivot is 0, i.e. moment of R about pivot is 0. This is a common thing to do in physics to eliminate unknown forces, so as to cut down on the number of unknowns.
Clockwise moments = 300x + 8W
Anti-clockwise moments = 760 * 5
At equilibrium, clockwise moments = anti-clockwise moments
300x + 8W = 3800 --------------------------- (2)
Sub (1) into (2):
800 + 2W + 8W = 3800
10W = 3000
W = 300
Hence, the weight of the boy is 300 N
