June 2023 Paper 3 Mechanics Q2

EdexcelCurrent spec4 marksForces & Newton's Laws Resolving Forces

Figure 1: particle P of mass 5 kg on a horizontal line, with a force of 28 N to the right and a force F N to the left — Figure 1

A particle \(P\) has mass 5 kg.

The particle is pulled along a rough horizontal plane by a horizontal force of magnitude 28 N.

The only resistance to motion is a frictional force of magnitude \(F\) newtons, as shown in Figure 1.

(a) Find the magnitude of the normal reaction of the plane on \(P\) (1)

The particle is accelerating along the plane at \(1.4\ \text{m s}^{-2}\)

(b) Find the value of \(F\) (2)

The coefficient of friction between \(P\) and the plane is \(\mu\)

Mark scheme (a)

Scheme	Marks	AO
Resolve vertically, \(R = 5g = 49\) (N)	B1	1.1b
	(1)

Notes

B1: Allow either \(5g\) or 49. No penalty for using \(g = 9.81\) or 10.
Ignore any working. Must be a positive number.
B0 if \(m\) is involved.
N.B. Could be seen on a diagram, provided it’s clearly the reaction.

Mark scheme (b)

Scheme	Marks	AO
Equation of motion: \(28 - F = 5 \times 1.4\)	M1	3.1a
\(F = 21\)	A1	1.1b
	(2)

Notes

M1: Equation with correct terms, dimensionally correct, condone sign errors.

A1: cao but allow \(\dfrac{15g}{7}\). Ignore units.

Mark scheme (c)

Scheme	Marks	AO
\(\mu = 0.43\) (2sf required)	B1 ft	3.4
	(1)
	(4 marks)

Notes

B1ft: \(\mu = \dfrac{\text{their (b)}}{\text{their (a)}}\). Answer must be a positive number given to 2sf.
N.B.
B0 if they use \(g = 9.81\) or 10 in this part of the question.
Do not allow restarts.
Allow \(\mu > 1\).