Circular motion question
A car is travelling on a horizontal racetrack round a circular bend of radius 40 m.
The coefficient of friction between the car and the road is 2/5.
(a) Find the maximum speed at which the car can travel round the bend without slipping,
giving your answer correct to 3 significant figures.
The owner of the track decides to bank the corner at an angle of 25° in order to enable the cars to travel more quickly.
(b) Show that this increases the maximum speed at which the car can travel round the bend without slipping by 63%, correct to the nearest whole number.
I'm sure the questions would be fine if I could correctly visualize them, but I'm not getting it. Why is friction the centripetal force in either case? It should be acting in a direction opposite to the car's motion, so how is it suddenly perpendicular (so as to act towards the centre of the circular bend)?
The coefficient of friction between the car and the road is 2/5.
(a) Find the maximum speed at which the car can travel round the bend without slipping,
giving your answer correct to 3 significant figures.
The owner of the track decides to bank the corner at an angle of 25° in order to enable the cars to travel more quickly.
(b) Show that this increases the maximum speed at which the car can travel round the bend without slipping by 63%, correct to the nearest whole number.
I'm sure the questions would be fine if I could correctly visualize them, but I'm not getting it. Why is friction the centripetal force in either case? It should be acting in a direction opposite to the car's motion, so how is it suddenly perpendicular (so as to act towards the centre of the circular bend)?
Original post by Big-Daddy
A car is travelling on a horizontal racetrack round a circular bend of radius 40 m.
The coefficient of friction between the car and the road is 2/5.
(a) Find the maximum speed at which the car can travel round the bend without slipping,
giving your answer correct to 3 significant figures.
The owner of the track decides to bank the corner at an angle of 25° in order to enable the cars to travel more quickly.
(b) Show that this increases the maximum speed at which the car can travel round the bend without slipping by 63%, correct to the nearest whole number.
I'm sure the questions would be fine if I could correctly visualize them, but I'm not getting it. Why is friction the centripetal force in either case? It should be acting in a direction opposite to the car's motion, so how is it suddenly perpendicular (so as to act towards the centre of the circular bend)?
The coefficient of friction between the car and the road is 2/5.
(a) Find the maximum speed at which the car can travel round the bend without slipping,
giving your answer correct to 3 significant figures.
The owner of the track decides to bank the corner at an angle of 25° in order to enable the cars to travel more quickly.
(b) Show that this increases the maximum speed at which the car can travel round the bend without slipping by 63%, correct to the nearest whole number.
I'm sure the questions would be fine if I could correctly visualize them, but I'm not getting it. Why is friction the centripetal force in either case? It should be acting in a direction opposite to the car's motion, so how is it suddenly perpendicular (so as to act towards the centre of the circular bend)?
perhaps you should draw a diagram of the set up from above?
basic circular motion tells us that when the car is going around a circular bend it's being accelerated towards the centre of the circle, which is to say centripetally . If the cars speed is constant the centripetal acceleration is constant and comes from a constant centripetal force.
that centripetal force comes from the friction between the tyres and the track surface.
Original post by Joinedup
basic circular motion tells us that when the car is going around a circular bend it's being accelerated towards the centre of the circle, which is to say centripetally . If the cars speed is constant the centripetal acceleration is constant and comes from a constant centripetal force.
that centripetal force comes from the friction between the tyres and the track surface.
basic circular motion tells us that when the car is going around a circular bend it's being accelerated towards the centre of the circle, which is to say centripetally . If the cars speed is constant the centripetal acceleration is constant and comes from a constant centripetal force.
that centripetal force comes from the friction between the tyres and the track surface.
Ok so the car is essentially a point on the surface of a circle. The friction should be antiparallel to the motion of the car - that is, tangential to the circle. How can it be centripetal then - it seems to be tangential i.e. perpendicular to the centripetal?
There is also friction acting towards the centre. Have you ever tried to push a car sideways? What's preventing it from moving?
Original post by Big-Daddy
Ok so the car is essentially a point on the surface of a circle. The friction should be antiparallel to the motion of the car - that is, tangential to the circle. How can it be centripetal then - it seems to be tangential i.e. perpendicular to the centripetal?
IMO stop thinking about 'motion' and think about velocity and acceleration instead.
the tangent of the circle IS parallel to the velocity of the car - the car is not changing it's distance from the centre of the circle over time.
if you were twirling a stone on a piece of string in a horizontal circle above your head, the tension in the string would be providing the centripetal force. it should be pretty clear that the stone would fly off at a tangent if the string broke, removing the centripetal force.
if it's a car being driven round in a circle something must be preventing it from carrying on in a straight line, the centripetal force must be coming from the friction between the tyres and the road, mustn't it?
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