WJEC Physics for A2: Student Bk

16 Unfortunately, adding this fictitious force can lead to correct results even if the physics is wrong. The red dotted force in Fig. 3.1.14 is this ‘centrifugal force’. If a student argues that the three forces, F , mg and F C are in equilibrium, the triangle of forces can be used to calculate F C . By a sleight of hand this then becomes the centripetal force which can be equated to mr ω 2 : two errors leading to a ‘correct’ answer. (b) An additional centripetal force When solving physics problems, e.g. the swing carousel, students are often tempted to include an additional centripetal force over and above the actual forces. This would complicate the carousel force diagram even more. The important thing to remember is that there is no separate centripetal force: it is the resultant of all the forces on the rotating object. 3.1.6 Some nice problems (a) Loop-the-loop Whether the question is about toy cars, marbles or an aircraft in flight, the principle of the question is exactly the same. v r Fig. 3.1.15 Loop-the-loop cars on a track How fast does the car (or marble, or plane) have to go to stay in the loop? We’ll examine the critical situation at the top of the curve. Supposing for the moment that the car remains on the track, what forces are acting? • Gravity, mg , downwards • The normal contact force, C , downwards. As these are the only forces acting and they are both in the direction of the centre of the circle then the sum of them is the centripetal force. ∴ mv 2 r = mg + C C cannot be less than zero (the track doesn’t hold on to the car), so for the car to maintain contact with the track, mv 2 r ≥ mg ∴ v ≥ √ rg mg F axis of rotation F C Fig. 3.1.14 Swing carousel rider with fictitious force Study point In simple questions, the loop-the- loop car in Fig. 3.1.15 is unpowered and frictionless. However, its speed is not constant because of the changing gravitational potential energy. If we are careful we can still use our constant speed equations to answer the question. Fig. 3.1.16 Forces at the top of the loop 3.1.9 Self-test A model car track has a radius of 20 cm. Calculate the minimum speed needed at the top of the loop. Fig. 3.1.17 Forces at the bottom of the loop mg v C mg v C' WJEC Physics for A2 Level: Unit 3