WJEC Physics for A2: Student Bk

15 3.1 Circular motion Example Estimate the maximum safe speed for a car to drive around a tight bend on a country lane, which has a radius of curvature of 20 m , if the road is dry. Answer Assuming that μ = 1. The only horizontal force on the car with a component along the radius of the bend is provided by the grip on the tyres. So this provides the necessary centripetal force. The maximum grip F max = μ C = 1.0 mg With a speed of v , the centripetal force = mv 2 = mv 2 r 20 m ∴ At the maximum speed mv 2 20 m = 1.0 m × 9.81 m s –2 ∴ Cancelling and re-arranging: v max = √ 20 m × 9.81 m s –2 = 14 m s − 1 3.1.5 Two common misconceptions (a) Centrifugal force When a car goes quickly round a bend, passengers ‘feel’ a force throwing them to the outside of the bend. Similarly in the fairground ride, the ‘cage’, the punters ‘feel’ a force pushing them onto the wall. This sensation is interpreted as indicating the existence of an outward acting force, hence centrifugal [Lat: fleeing the centre]. This is an understandable interpretation but it is false – there is no outward force, but there is an inward force, as we have seen, which somehow the passengers are ignoring. Suppose (for the moment) that there were an outwards pushing force: what external body is exerting this force on the people and what is its N3 partner force? This misinterpretation is not confined to rotations: Fig. 3.1.13 is of a (cartoon) airline passenger, but it could equally be a car passenger. The aeroplane is accelerating to the left for takeoff. For twenty seconds or so the seat exerts a forward force on the passenger which accelerates him to take-off speed. But what does the passenger ‘feel’? He ‘feels’ pressed backwards into the seat. The whole problem is trying to apply Newton’s laws of motion in an accelerated frame of reference (accelerating plane or rotating car). It is possible to do so by inventing additional, ‘fictitious’ forces. 2 However at A level, we’ll stick to inertial (non-accelerating) frames of reference. There is a similar effect with gravity and weight. There is no sensation of weight if gravity is the only force on us, as in the ISS or during a dive from a high board. We know that gravity is exerting its ineluctable tentacles on us but we are only aware of it when we are stopped from falling freely by the upward force of the floor or a chair. So the downward sensation of weight arises from the compression of our tissues between the normal contact force (which is upwards) and the sensationless downward force of gravity. So the apparently outwards force on the cage passengers is a psychological misinterpretation. 3.1.7 Self-test Repeat the calculation in the example for a wet road. 3.1.8 Self-test Why do the answers to the example and Self-test 3.1.7 not depend upon the mass of the car? Fig. 3.1.12 The ‘cage’ Fig. 3.1.13 Force on an accelerating passenger Forward acceleration 2 Another fictitious force, beloved of meteorologists, is the Coriolis force, which they use to explain the circular motion of air around low and high pressure regions.