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.

1. STARTER – label the forces on a car

2. Tight Corners 2
Physics in Sport

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.

4. Italian Job

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

9. Road Banking

10. Road Banking Forces
(We assume that frictional forces are now minimal)
 Vertical forces must balance
Fncosθ=mg
Fn =
mg
cosθ

11. Road Banking Forces
(We assume that frictional forces are now minimal)
 Horizontal forces provide the
centripetal force
Fnsinθ= mv2
r

12. Deriving the formula
Fnsinθ= mv2
r
mg sinθ= mv2
cosθ
r
sinθ= v2
cosθ rg
tanθ= v2
rg

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?