A-level · Forces & Newton's laws

Connected particles on slopes and pulleysExam-style questions

Two particles joined by a light inextensible string over a smooth pulley — one on a slope, one hanging — share the same acceleration and string tension; write F = ma along each particle's line of motion (including the slope component and friction) and solve simultaneously.

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18 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 3 Level 4 Level 5

1
A particle of mass $4$ kg on a smooth slope of $30^\circ$ is connected by a light string over a smooth pulley at the top to a $6$ kg mass hanging freely. Find
(a) the acceleration and (b) the tension, to 3 s.f. ( $g = 9.8$ .)
Level 3 · 4 marksTry it
2
A particle of mass $7$ kg on a smooth slope of $25^\circ$ is connected over a smooth pulley to a $4$ kg mass hanging freely. Find the acceleration, to 3 s.f. ( $g = 9.8$ .)
Level 3 · 2 marksTry it
3
A particle of mass $5$ kg on a rough slope of $30^\circ$ ( $\mu = 0.2$ ) is connected over a smooth pulley to a $4$ kg mass hanging freely. Find
(a) the acceleration and (b) the tension, to 3 s.f. ( $g = 9.8$ .)
Level 3 · 4 marksTry it
4
A particle of mass $4$ kg on a rough slope of $30^\circ$ is connected over a smooth pulley to a $5$ kg hanging mass. The system accelerates at $2\ \text{m s}^{-2}$ , with the $5$ kg mass descending. Find the coefficient of friction, to 3 s.f. ( $g = 9.8$ .)
Level 3 · 2 marksTry it
5
A particle of mass $3$ kg on a smooth slope of $40^\circ$ is connected over a smooth pulley to a $2$ kg hanging mass. Determine whether the system moves, and if so find the acceleration, to 3 s.f. ( $g = 9.8$ .)
Level 3 · 2 marksTry it

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