A-level · Forces & Newton's laws

Connected particlesExam-style questions

Why two bodies joined by a light inextensible string share one acceleration and one tension, the two-step method that runs every problem — whole system for the acceleration, a single body for the internal force — and why the connecting force is internal to the system but external to each body.

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13 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 car of mass $1200$ kg tows a trailer of mass $300$ kg along a straight horizontal road, connected by a light rigid tow-bar. The car's engine produces a driving force of $2700$ N. The resistances to motion are $400$ N on the car and $200$ N on the trailer, and these are modelled as constant.
(a) Find the acceleration of the car and trailer. (3 marks)
(b) Find the tension in the tow-bar. (3 marks)
(c) When the car and trailer are travelling at $20$ m s⁻¹, the tow-bar breaks. Assuming the resistance on the trailer is unchanged, find the distance the trailer travels after the tow-bar breaks before coming to rest. (2 marks)
Level 3 · 8 marksTry it
2
Two particles $A$ ( $3$ kg) and $B$ ( $2$ kg) are joined by a light inextensible string on a smooth horizontal table. A horizontal force of $15$ N is applied to $B$ , away from $A$ .
(a) Find the acceleration of the system.
(b) Find the tension in the string.
Level 3 · 4 marksTry it
3
A car of mass $1000$ kg tows a trailer of mass $500$ kg along a straight level road. The engine provides a driving force of $4500$ N and there is no resistance.
(a) Find the acceleration.
(b) Find the tension in the tow bar.
Level 3 · 4 marksTry it
4
A locomotive of mass $6000$ kg pulls a single carriage of mass $4000$ kg. The driving force is $25000$ N and resistances are negligible.
(a) Find the acceleration.
(b) Find the force in the coupling.
Level 3 · 4 marksTry it
5
A car of mass $1200$ kg tows a trailer of mass $400$ kg. The driving force is $4000$ N, and resistances of $600$ N (car) and $200$ N (trailer) act. Find
(a) the acceleration and (b) the tension in the tow bar.
Level 3 · 4 marksTry it

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