October 2021 Paper 1 Q9

OCR MEICurrent spec8 marksConnected Particles Forces & Newton's Laws

9 The diagram shows a toy caterpillar consisting of a head and three body sections each connected by a light inextensible ribbon. The head has a mass of 120 g and the body sections each have a mass of 90 g.

The toy is pulled on level ground using a horizontal string attached to the head. The tension in the string is 12 N. There are resistances to motion of 2.5 N for the head and each section of the body.

Toy caterpillar on level ground: three body sections on the left joined in a line to the head on the right, with a horizontal string attached to the head

(a)

(i) State the equation of motion for the toy caterpillar modelled as a single particle. [2]

(ii) Calculate the acceleration of the toy caterpillar. [1]

(b) Draw a diagram showing all the forces acting on the head of the toy caterpillar. [3]

Mark scheme (a)

Scheme	Marks	AO
(i) Total mass 390 g (0.390 kg) \(12 - 4 \times 2.5 = 0.390a\)	M1 A1	3.3 3.3
	[2]
(ii) \(5.13\ \text{m}\,\text{s}^{-2}\)	B1	1.1b
	[1]

Notes

(i) M1: Newton’s second law; condone missing or incorrect resistance or incorrect total mass
Allow for \(T - R = ma\) if the correct substitution of values seen in part 9aii

A1: Fully correct equation need not be simplified

(ii) B1: cao

Force diagram for the head: R upwards, 0.12g N downwards, 12 N to the right, and to the left the tension [in the ribbon] and 2.5 N — Mark scheme (b)

Scheme	Marks	AO
	B1 B1 B1	1.1b 1.1b 1.1b
	[3]

Mark scheme (c)

Scheme	Marks	AO
N2L for the head only \(12 - 2.5 - T = 0.12a\) OR N2L for the three body sections together \(T - 3 \times 2.5 = 0.270a\)	M1	1.1b
\(T = 8.88\) N	A1	1.1b
	[2]

Notes

M1: N2L with correct mass and their acceleration. Allow missing or incorrect resistance
Allow for mass in grams if same error seen in part (a)

A1: cao
Allow A1 for correct answer from consistent use of grams