STARTER – label the forces on a car

Tight Corners 2 Physics in Sport

Learning Intentions

Identify vertical and horizontal forces on a vehicle moving at constant velocity

Explain that when a vehicle travels around a banked curve the horizontal component of the normal force provides the centripetal force.

Derive and use tanθ=v2/rg for banked curves.

Italian Job

Forces on a moving vehicle (at a constant speed)

FR FD

FN1 FN2

W

Horizontally

Vertically

FN

Tell me about the forces Express in maths

Forces on a car when cornering

Centripetal forces are from friction between the road an the tyres of the car

Resistive and driving forces are not shown

r

vmF

2

Coefficient of Friction

The friction between a moving vehicle/person and the ground is determined by a number of factors.

Weight

Surface contact

Surface conditions etc.

The reaction force “available” for friction is referred to as the coefficient of friction.

Ff= friction force (N)

FN= Normal (reaction) force (N)

μf= coefficient of friction

𝐹𝑓 = 𝜇𝑓𝐹𝑁

Centripetal Force Calculation

150 kg

1. Calculate the centripetal force acting on this motor racer.

2. Find the coefficient of friction.

835N 0.57

Road Banking

Road Banking Forces (We assume that frictional forces are now minimal)

Vertical forces must balance

Fncosθ=mg

Fn = mg

cosθ

Road Banking Forces (We assume that frictional forces are now minimal)

Horizontal forces provide the centripetal force

Fnsinθ= mv2

r

Deriving the formula

Fnsinθ= mv2

r

mg sinθ= mv2

cosθ r

sinθ= v2

cosθ rg

tanθ= v2

rg

Calculations

A road is to be constructed with a bend of radius 200m. It will be banked so that the cars travelling up to 100km/h will not rely on friction. What banking angle is necessary?