On the road

Question 1

How is resultant force as a vehicle travels over the top of a hill measured?

Answer 1

• support force, S, from the road on the vehicle is directly upwards in the opposite direction to its weight, mg.
• The resultant force on the vehicle is the difference between the weight and the support force
• this difference acts towards the centre of curvature of the hill as the centripetal force
• mg - S = mv² / r

Question 2

When is the support force zero? then what is the equation used to describe the support force?

Answer 2

the vehicle would lose contact with the road if its speed is equal to or greater than a particular speed, V₀

if this happens the support force is then zero

so mg = mv₀² / r

Question 3

Going around the roundabout what is the limiting force of friction?

Answer 3

F₀ = mv₀² / r

for no skidding to occur, the force of friction between the tryres and the road surface must be less than a limiting value, F0, which is propotional to the vehicles weight

Question 4

Why are motorway sliproads banked where it is curved?

Answer 4

motorway slip roads often bend in a tight cuurve

such a road is usually banked to enable vehicles to drive around without any sideways friction acting on the tyres

Question 5

What happens with no banking?

Answer 5

the centripetal froce on a vehicle is provided only by the sideways friction between the vehicle and the road surface

a vehicle on a bend slips outwards if its speed is too high

Question 6

What happens on a banked road?

Answer 6

speed can be higher

for there to be no sideway friction, the horizontal components of the support forces must act as the centripetal force

Question 7

What is the equation for a car that is on a bank?

Answer 7

S1 and S2 are the support forces - caused by tyres

(1) (S₁ + S₂) sin ϴ is the horizontal component
(2) (S₁ + S₂) cos ϴ is the vertical

because (1) acts as the centripetal force (1) = mv² / r

because (2) balances the weight - (2) = mg

Question 8

What is the equation for tanϴ?

Answer 8

(S₁ + S₂) sin ϴ / (S₁ + S₂) cos ϴ = mv² / mgr = v² / gr

Question 9

there is no sideways friction if speed v is such that…

Answer 9

v² = g r tanϴ

Question 10

What is teh equation for the support force for a dipping ride at the bond of a dip radius

Answer 10

S = mg + mv2 / r

centripetal force acts in attidition to gravity

this would be the opposite at the top of the curve