AS June 2023 Q3

EdexcelCurrent spec9 marksHorizontal Circular Motion

3. A girl is cycling round a circular track.
The girl and her bicycle have a combined mass of 55 kg.
The coefficient of friction between the track surface and the tyres of the bicycle is \(\mu\).

The track is banked at an angle of \(15^\circ\) to the horizontal.

The girl and her bicycle are modelled as a particle moving in a horizontal circle of radius 50 m
The minimum speed at which the girl can cycle round this circle without slipping is \(4.5\ \text{m s}^{-1}\)

Using the model, find the value of \(\mu\). (9)

force diagram: particle on a slope at 15 degrees to the horizontal, 50 m from the centre of the circle, with R perpendicular to the slope, F up the slope and 55g vertically down — Mark scheme

Scheme	Marks	AO

They need to form two equations, they could be in either order. Mark in the order seen.
Equation of motion horizontally	M1	3.4
\(\dfrac{55 \times 4.5^2}{50} = R\sin 15^\circ - F\cos 15^\circ\)	A1 A1	1.1b 1.1b
Resolve vertically	M1	3.4
\(55g = R\cos 15^\circ + F\sin 15^\circ\)	A1ft A1ft	1.1b 1.1b
Uses \(F = \mu R\)	B1	1.2
Solve for \(\mu\)	dM1	3.1b
\(\mu = 0.22\) or \(\mu = 0.224\)	A1	2.2a
	(9)
	(9 marks)

Notes