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
Figure 3 shows a block $A$ of mass $4$ kg lying on a rough horizontal table. The block is attached to one end of a light inextensible string which passes over a smooth pulley fixed at the edge of the table. The other end of the string is attached to a block $B$ of mass $3$ kg, which hangs freely.Figure 3 (not accurately drawn)

The coefficient of friction between $A$ and the table is $0.25$ . The system is released from rest with the string taut.
(a) Find the acceleration of the system and the tension in the string. (7 marks)
(b) $B$ hits the ground after falling $1.5$ m. Find the speed of $B$ as it hits the ground, giving your answer to $3$ significant figures. (3 marks)
(c) After $B$ hits the ground the string becomes slack and $A$ continues to move. Find the further distance $A$ travels before coming to rest, giving your answer to $3$ significant figures. (2 marks)
Level 5 · 12 marksTry it
2
In a physics experiment, two trolleys, $A$ and $B$ , are joined by a light rigid bar. The trolleys stand on a horizontal bench, with $B$ directly behind $A$ .

Trolley $A$ has a mass of $1.5$ kilograms and trolley $B$ has a mass of $1.4$ kilograms.

A student pulls a string that is attached to the front of trolley $A$ . The string is held at an angle of $25^\circ$ above the horizontal and its tension is $4$ newtons.

Starting from rest, the trolleys move along the bench in a straight line with acceleration $0.25\ \text{m s}^{-2}$ , as shown in the diagram below.A resistance force of $1.2$ N acts on trolley $A$ throughout its motion.
(a) Show that trolley $B$ is subject to a resistance force of approximately $1.7$ N

(4 marks)
(b) When the speed of the trolleys reaches $0.8\ \text{m s}^{-1}$ , the student lets go of the string.

The trolleys then slow down at a constant rate until they stop, having travelled a further $h$ metres.

You may assume that the resistance forces on the trolleys stay the same as before.
(b) (i) Find the tension in the bar while the trolleys are slowing down.

(ii) Find $h$

(7 marks)
(c) State one way in which the bar has been modelled in your answer to part (b)(i).

(1 mark)
Level 5 · 12 marksTry it