A-LevelMathematicsMechanics9709/42 · May/June 2021 · Q36 Marks
A ring of mass 0.3 kg is threaded on a horizontal rough rod. The coefficient of friction between the ring and the rod is 0.8. A force of magnitude 8 N acts on the ring. This force acts at an angle of 10° above the horizontal in the vertical plane containing the rod.
- Find the time taken for the ring to move, from rest, 0.6 m along the rod.[6]
Mark scheme
Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.
- [M1] Resolving along or perpendicular to the rod 3 terms in either direction
- [A1] 8sin10+R=0.3g
- [A1] 8cos10-F=0.3a
- [M1] F=0.8R [R=1.61081..., F =1.28865...] Using F = μR, where R is 2 terms involving weight and a component of 8 N.
- [M1] [a=21.966...] Complete method leading to an equation in t such as s = ut + 1/2 at^2 with s = 0.6, u = 0 and using their value of a found from a Newton's second law with 3 terms, namely, component of 8 N, any friction and 0.3a.
- [A1] t=0.234 seconds Allow use of a = 22 for M1 and A1
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