A-LevelMathematicsMechanics9709/51 · Oct/Nov 2019 · Q69 Marks
A and B are two fixed points on a vertical axis with A 0.6 m above B. A particle P of mass 0.3 kg is attached to A by a light inextensible string of length 0.5 m. The particle P is attached to B by a light elastic string with modulus of elasticity 46 N. The particle P moves with constant angular speed 8 rad s⁻¹ in a horizontal circle with centre at the mid-point of AB.
- (i)Find the speed of P.[2]
- (ii)Calculate the tension in the string BP and hence find the natural length of this string.[7]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2019). The mark or mark type is shown in brackets.
- [B1] Use Pythagoras's theorem
- [B1] Use v = rω
- [B1] Resolve vertically
- [M1A1] Use Newton's Second Law horizontally
- [M1] Attempt to solve for B
- [A1] B=2.3 N
- [M1] Use T = λx/l and attempt to solve
- [A1] L = 0.476 m or 10/21
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