This document discusses forces acting on vehicles, including centripetal force. It explains that when a vehicle travels around a banked curve, the horizontal component of the normal force provides the centripetal force. The document derives the formula tanθ=v2/rg for calculating the banking angle required so that friction is not needed to provide the centripetal force when traveling around a curved road. An example calculation is provided to find the banking angle needed for a road with a 200m radius bend that will allow cars to travel up to 100km/h.
3. 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.
5. Forces on a moving vehicle (at a constant speed)
FN
Horizontally
Vertically
FN1
FN2
FR
FD
Tell me about the forces
Express in maths
W
6. Forces on a car when cornering
2
v
F m
r
Centripetal forces are from
friction between the road an
the tyres of the car
Resistive and driving forces
are not shown
7. 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 = 𝜇 𝑓 𝐹 𝑁
8. Centripetal Force Calculation
150 kg
1. Calculate the
centripetal force acting
on this motor racer.
2. Find the coefficient of
friction.
835N
0.57
13. 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?