A-LevelMathematicsMechanics9709/41 · May/June 2017 · Q36 Marks
Two light inextensible strings are attached to a particle of weight 25 N. The strings pass over two smooth fixed pulleys and have particles of weights A N and BN hanging vertically at their ends. The sloping parts of the strings make angles of 30° and 40° respectively with the vertical (see diagram). [Figure 3.1] The system is in equilibrium. Find the values of A and B.
- Two light inextensible strings are attached to a particle of weight 25 N. The strings pass over two smooth fixed pulleys and have particles of weights A N and BN hanging vertically at their ends. The sloping parts of the strings make angles of 30° and 40° respectively with the vertical (see diagram). The system is in equilibrium. Find the values of A and B.[6]
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Mark scheme
Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.
- EITHER: (M1 Resolve horizontally and/or vertically at the 25 N weight)
- A cos 30 + B cos 40 = 25
- A sin 30 = B sin 40
- (M1 Solve for A and/or B)
- A = 17.1
- B = 13.3
- OR: (M1 Attempt Lami's theorem)
- 25/sin 70 = A/sin 140 = B/sin 150 (One correct equation)
- A second correct equation
- (M1 Solve for A and/or B)
- A = 17.1
- B = 13.3
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