A-LevelPhysicsForces, density and pressure9702/23 · Oct/Nov 2019 · Q15 Marks

A uniform square sheet of card ABCD is freely pivoted by a pin at a point P. The card is held in a vertical plane by an external force in the position shown in Fig. 1.1. [Figure 1.1] The card has weight 0.15N which may be considered to act at the centre of gravity G. Each side of the card has length 17cm. Point P lies on the horizontal line AC and is 4.0cm from corner A. Line BD is vertical. The card is released by removing the external force. The card then swings in a vertical plane until it comes to rest.

(a)Determine the SI base units of the moment of a force.[1]
(b)(i)Calculate the magnitude of the resultant moment about point P acting on the card immediately after it is released.[2]
(b)(ii)Explain why, when the card has come to rest, its centre of gravity is vertically below point P.[2]

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Mark scheme

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[1] base units: kg m s-2 × m = kg m² s-2
[1] distance of COG from P (= GP) = 17 cos 45° – 4.0 or (144.5)½ – 4.0 (= 8.0 cm)
[1] moment = 0.15 × 8.0 × 10-2 = 1.2 x 10-2 Nm
[1] (line of action of) weight acts through pivot/P or distance between (line of action of) weight and pivot/P is zero
[1] (so) weight does not have a moment about pivot/P

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