1. 1. A car of mass 1000 kg is driving into a corner of radius 50m at a speed of 20 ms -1. The coefficient of friction between the road and the car’s tyres is 0.8. Will the car skid ? The centripetal force needed to make the car go round the corner is equal to the friction force available, so the car is exactly on the point where it will start to skid.

2. 2. The diagram shows an aircraft which is banked at an angle of 22º to the horizontal in order to follow a circular path with a radius of 500m. a. Draw a ‘free body’ diagram for the aircraft in this situation. c. Calculate the speed of the aircraft. mg L (Lift) b. Draw a vector diagram to show how the forces add. mgL C From the vector diagram : But

3. 3. A mass ‘m’ is constrained to move in a circle with velocity ‘v’ by a string which makes an angle  with the horizontal. This angle decreases as the velocity of the mass increases. 1. Sketch a free body diagram showing the forces on the mass when  is about 30  2. Add a thick arrow to the diagram showing the direction of the acceleration of the mass, and label this arrow with the magnitude of the acceleration. 3. Hence show that the angle  is given by the formula: mg T Horizontal component of T causes the acceleration towards the centre of the circle Vertical component of T holds the mass up against gravity Divide 2nd equation by 1st. This is f = ma

4. 1. A car of mass 1000 kg is driving into a corner of radius 50m at a speed of 20 ms -1. The coefficient of friction between the road and the car’s tyres is 0.8. Will the car skid ?

5. 1. The diagram shows an aircraft which is banked at an angle of 22º to the horizontal in order to follow a circular path with a radius of 500m. a. Draw a ‘free body’ diagram for the aircraft in this situation. c. Calculate the speed of the aircraft. b. Draw a vector diagram to show how the forces add.

6. 2. A mass ‘m’ is constrained to move in a circle with velocity ‘v’ by a string which makes an angle  with the horizontal. This angle decreases as the velocity of the mass increases. 1. Sketch a free body diagram showing the forces on the mass when  is about 30  2. Add a thick arrow to the diagram showing the direction of the acceleration of the mass, and label this arrow with the magnitude of the acceleration. 3. Hence show that the angle  is given by the formula: