Question

Question 2 A small car is driving in a horizontal circle on the inside surface of a cone as shown. The car has mass M and is moving with a constant speed of V. Assume there is no friction acting on the car. The horizontal circle is located at a height H above the point of the cone as shown. The angle between the centre of the cone and the side (the half angle) is ? as shown. a) Draw a free body diagram showing all the forces acting on the car. Also, draw a labelled arrow to indicate the direction of any acceleration. 3 marks] b) What force is causing this car to remain at a constant height H within the cone? Explain. arkl and the acceleration of gravity, g, find c) In terms of the given quantities (M, V, Hand the value of the normal force acting on the car. 4 marks] d) In terms of the given quantities (M, H and 8) and acceleration of gravity,g, find the value of the constant speed V for which the car can continue to move in a horizontal circle at height H with no friction along the incline. (Hint: ifyou do the physics, trigonometry and algebra correctly, the trig functions cancel and the answer is independent of ?) 5 marks

Answer 1

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a) N_0 = normal contact for Mg = Weight b) The normal contact force c) N cos theta = MV^2/r (1) N sin theta = Mg (11) r = H tan theta Therefore N^2 = (MV^2/H tan theta)^2 + (Mg)^2 (From (i) and (ii)) or N = M squareroot (V^4/H^2 tan^2 theta) + g^2 d) from (i) and (ii) tan theta = Mg r/MV^2 = gr/V^2 = g H tan theta/V^2 or V = squareroot gH