A car of mass 1200 kg takes a bend of radius 50 m at 15 m s⁻¹. Calculate the centripetal force needed.

F = mv²/r = 1200 × (15)²/50 = 1200 × 225/50 = 5.4 × 10³ N, directed towards the centre of the bend.

Explain why a car is more likely to skid on a bend when the road is wet.

Water reduces the frictional force available between the tyres and the road. If the maximum friction falls below mv²/r the car cannot be turned tightly enough and it continues along a path of larger radius, leaving the bend.

Why must a driver slow down for a tighter bend if the available friction is unchanged?

The force required is mv²/r, which increases as r falls, so the speed must be reduced to keep the required force within what friction can supply.

CCEA A-Level Physics 1210

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Uniform Circular Motion

Applying F = mv²/r to motion at constant speed

3 things to know
Unit A2 1

Overview

Recall questions on what supplies the centripetal force in each case — a whirled stone, a car on a level bend, a satellite, a conical pendulum — with worked force and acceleration calculations, the greatest speed a bend can be taken at, and the difference between a banked and a level bend.

What you need to know

Answer each one before you reveal it.

Your recallNot started

Key term

What provides the centripetal force on a stone whirled in a horizontal circle on the end of a string?

Key term

What provides the centripetal force on a car rounding a level bend?

Numbers

Calculate the centripetal acceleration of a car of mass 1200 kg taking a bend of radius 50 m at 15 m s⁻¹.

Questions from this subtopic

Each one with the model answer underneath.

1
What provides the centripetal force on a stone whirled in a horizontal circle on the end of a string?
Model answer
The tension in the string provides the centripetal force, acting along the string towards the centre of the circle.
2
What provides the centripetal force on a car rounding a level bend?
Model answer
Friction between the tyres and the road surface acts sideways towards the centre of the bend and supplies the centripetal force.
3
A car of mass 1200 kg takes a bend of radius 50 m at 15 m s⁻¹. Calculate the centripetal force needed.
Model answer
F = mv²/r = 1200 × (15)²/50 = 1200 × 225/50 = 5.4 × 10³ N, directed towards the centre of the bend.
4
Calculate the centripetal acceleration of a car of mass 1200 kg taking a bend of radius 50 m at 15 m s⁻¹.
Model answer
a = v²/r = 225/50 = 4.5 m s⁻², directed towards the centre of the bend.
5
Explain why a car is more likely to skid on a bend when the road is wet.
Model answer
Water reduces the frictional force available between the tyres and the road. If the maximum friction falls below mv²/r the car cannot be turned tightly enough and it continues along a path of larger radius, leaving the bend.
6
Why must a driver slow down for a tighter bend if the available friction is unchanged?
Model answer
The force required is mv²/r, which increases as r falls, so the speed must be reduced to keep the required force within what friction can supply.

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