THE TURNING EFFECT OF FORCES
4 marks · NormalThe diagram shows a uniform beam of length 2.0 m and negligible mass balanced on two supports, A and B, at either end. A box of mass 20 kg is placed 0.5 m from support A.
Draw a force diagram showing the forces acting on the beam.
Taking moments about support A, calculate the upward force on support B due to the box only. (Take g = 10 N/kg.)
State and explain how the upward forces at supports A and B would change if the box is moved closer to support B.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
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(a) — · must show weight of box acting down at 0.5 m from A, upward forces at A and B
(b) 50 N
(c) Upward force at B increases, at A decreases. This is because the box is nearer to B, so B supports more of its weight. · must show upward force at B increases, reason refers to closer position
Common mistakes: forgetting distances; using wrong pivot
Show mark scheme and worked solution
Marking points
B1 (a) · 1 mark · Correct forces labelled (box weight and upward forces)
M1 (b) · 1 mark · Sets up correct moment balance: (20 × 10) × 0.5 = F_B × 2.0
A1 (b) · 1 mark · F_B = 100 × 0.5 / 2.0 = 25/1 = 50 N
B2 (c) · 1 mark · Correctly states and explains force change as box moves
Worked solution
a) The force diagram should show:
— Downward force (weight of box, 200 N) at 0.5 m from A,
— Upward forces at A and B (unknown yet).
b) Taking moments about A:
c) As the box gets closer to B, B has to supply more of the upward force to balance the increased moment on its side, while A supplies less.