A-LevelMathematicsMechanics9709/51 · May/June 2018 · Q58 Marks
A particle P of mass 0.7 kg is attached by a light elastic string to a fixed point O on a smooth plane inclined at an angle of 30° to the horizontal. The natural length of the string is 0.5 m and the modulus of elasticity is 20 N. The particle P is projected up the line of greatest slope through O from a point A below the level of O. The initial kinetic energy of P is 1.8 J and the initial elastic potential energy in the string is also 1.8 J.
- (i)Find the distance OA.[2]
- (ii)Find the greatest speed of P in the motion.[6]
Mark scheme
Marking points from the official mark scheme (May/June 2018). The mark or mark type is shown in brackets.
- [M1] 1.8 = (20e²) / (2 × 0.5); Use T = λx / l (or EPE = λx² / (2l))
- [A1] e = 0.3, OA = 0.8
- [M1] 0.7gsin30 = 20x / 0.5; Use Newton's Second Law up the plane
- [A1] x = 0.0875 m
- [B1] EPE = 20×0.0875² / (2×0.5)
- [M1] 0.7v² / 2 = 1.8 + 1.8 - 0.7g(0.3-0.0875)sin30 - 20×0.0875² / (2×0.5); Attempt to set up a 5 term energy equation
- [A1] Correct equation
- [A1] v = 2.78 ms¯¹
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