THE TURNING EFFECT OF FORCES
6 marks · HardA uniform metal plank of length 2.5 m and mass 4.0 kg is placed horizontally across a small stream, resting on rocks at each end (points R and S). A stone of mass 2.0 kg is placed 0.75 m from end R, as shown.
Take gravitational field strength . Ignore the weight of the plank unless stated otherwise.
Calculate the upward force at support S when only the stone is on the plank. (Ignore the weight of the plank.)
Now include the weight of the plank. Calculate the new upward force at support S.
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.
Show answer
(a) Upward force at S = 13.07 N · must show moment about R, stone weight calculation, distance to S used
(b) Upward force at S = 31.3 N · must show moment about R, stone weight and plank weight included, centre of gravity position used
Common mistakes: Not including distance from pivot for the centre of gravity; Not combining moments correctly; Forgetting to multiply mass by g
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Correctly sets up moments about point R using only the stone.
A1 (a) · 1 mark · Accurately calculates upward force at S.
M2 (a) · 1 mark · Converts mass to weight (N).
M1 (b) · 1 mark · Sets up total moment equation including plank mass and stone.
A1 (b) · 1 mark · Identifies distance of centre of gravity as 1.25 m from R.
A2 (b) · 1 mark · Correctly calculates new upward force at S to 2 sf.
Worked solution
a) Take moments about point R. Let the upward force at S be F_S (N).
To 2 sf, F_S = 13 N or 13.1 N (using g = 9.8, 2 dp).
b) Now include plank weight (W = 4.0 × 9.8 = 39.2 N), centre of gravity at 1.25 m from R.
To 2 sf, F_S = 33 N (accept 33.3 N).