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

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- 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 = mv
^{2} / r

^{2}/ rWhen is the support force zero? then what is the equation used to describe the support force?

the vehicle would lose contact with the road if its speed is equal to or greater than a particular speed, V_{0}

if this happens the support force is then zero

so mg = mv_{0}^{2} / r

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

F_{0} = mv_{0}^{2} / 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

Why are motorway sliproads banked where it is curved?

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

What happens with no banking?

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

What happens on a banked road?

speed can be higher

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

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

S1 and S2 are the support forces - caused by tyres

(1) (S_{1} + S_{2}) sin ϴ is the horizontal component

(2) (S_{1} + S_{2}) cos ϴ is the vertical

because (1) acts as the centripetal force (1) = mv^{2} / r

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

What is the equation for tanϴ?

(S_{1} + S_{2}) sin ϴ / (S_{1} + S_{2}) cos ϴ = mv^{2} / mgr = v^{2} / gr

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

v^{2} = g r tanϴ

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

S = mg + mv2 / r

centripetal force acts in attidition to gravity

this would be the opposite at the top of the curve