A-LevelMathematicsMechanics9709/41 · Oct/Nov 2019 · Q47 Marks

Two blocks A and B of masses 4 kg and 5 kg respectively are joined by a light inextensible string. The blocks rest on a smooth plane inclined at an angle α to the horizontal, where tan α = 3/4. The string is parallel to a line of greatest slope of the plane with B above A. A force of magnitude 36 N acts on B, parallel to a line of greatest slope of the plane [Figure X.X].

(i)Find the acceleration of the blocks and the tension in the string.[5]
(ii)At a particular instant, the speed of the blocks is 1 m s⁻¹. Find the time, after this instant, that it takes for the blocks to travel 0.65 m.[2]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2019). The mark or mark type is shown in brackets.

[M1] Apply Newton's second law to either or to the system
[A1] Any two correct. Allow α = 16.3 used. (Block A: T - 4g × (3/5) = 4a; Block B: 36 - T - 5g × (3/5) = 5a; System: 36 - 5g × (3/5) - 4g × (3/5) = 9a)
[M1] Either solving the system for a or solving a pair of simultaneous equations for either a or T
[A1] a = 1.2 m s⁻²
[A1] T = 16 N
[M1] Use constant acceleration equation(s) with u = 1 and solve a 3 term quadratic equation to find t (0.65 = 1 × t + ½ × 1.2t²)
[A1] t = 0.5 s

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