A-LevelMathematicsMechanics9709/43 · May/June 2020 · Q59 Marks
A block B of mass 4 kg is pushed up a line of greatest slope of a smooth plane inclined at 30° to the horizontal by a force applied to B, acting in the direction of motion of B. The block passes through points P and Q with speeds 12ms⁻¹ and 8 ms⁻¹ respectively. P and Q are 10 m apart with P below the level of Q.
- (a)Find the decrease in kinetic energy of the block as it moves from P to Q.[2]
- (b)Hence find the work done by the force pushing the block up the slope as the block moves from P to Q.[3]
- (c)At the instant the block reaches Q, the force pushing the block up the slope is removed. Find the time taken, after this instant, for the block to return to P.[4]
Mark scheme
Marking points from the official mark scheme (May/June 2020). The mark or mark type is shown in brackets.
- [M1] Decrease in KE = ½ × 4 × (12² - 8²)
- [A1] 160 J
- [B1] PE gained = 4g × 10sin30 (= 200)
- [M1] Total work done = 200 – 160
- [A1 FT] Total work done = 40 J
- [M1] -4gsin30 = 4a
- [A1] a = -5
- [M1] -10 = 8t – ½ × 5t²
- [A1] t = 4.16 s
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