A-LevelMathematicsMechanics9709/52 · May/June 2017 · Q37 Marks
An open box in the shape of a cube with edges of length 0.2 m is placed with its base horizontal and its four sides vertical. The four sides and base are uniform laminas, each with weight 3 N.
- (i)Calculate the height of the centre of mass of the box above its base.[3]
- (ii)The box is now fitted with a thin uniform square lid of weight 3 N and with edges of length 0.2 m. The lid is attached to the box by a hinge of length 0.2 m and weight 2 N. The lid of the box is held partly open. Find the angle which the lid makes with the horizontal when the centre of mass of the box (including the lid and hinge) is 0.12 m above the base of the box.[4]
Mark scheme
Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.
- [B1] Height of C of M of each vertical face above the base = 0.1 m
- [M1] Takes moments about the base. y is the height of the C of M above the base
- [A1] y = 0.08 m
- [B1] θ is the angle the lid makes with the horizontal
- [M1] Take moments about the base
- [A1]
- [A1] θ = 41.8°
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