Centripetal acceleration and forceEdexcel International A Level Physics: Subtopic test

1. 1
   A ball of mass 0.25 kg is attached to a light string and whirled in a horizontal circle of radius 0.80 m on a frictionless table. The other end of the string is fixed at the centre of the circle and the ball moves at a constant speed of 4.0 m s⁻¹.

   (a)

   What is the direction of the acceleration of the ball at any instant?

   [1 mark]

   • AAlong the tangent to the circle, in the direction of motion
   • BRadially outwards, away from the centre
   • CRadially inwards, towards the centre
   • DThere is no acceleration because the speed is constant

   (b)

   Calculate the tension in the string.

   [1 mark]

   • A1.25 N
   • B5.0 N
   • C3.2 N
   • D20 N

   (c)

   The ball moves at constant speed. Explain why a resultant force acts on it and state the direction of that force.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A laboratory centrifuge spins at a steady 3000 revolutions per minute. A sample tube is held so that its contents are at a distance of 0.12 m from the axis of rotation.

   (a)

   What is the angular speed of the sample in rad s⁻¹?

   [1 mark]

   • A314
   • B50
   • C3000
   • D1.9 × 10⁴

   (b)

   What is the centripetal acceleration of the contents of the tube in m s⁻²?

   [1 mark]

   • A38
   • B8.2 × 10⁵
   • C1.1 × 10⁶
   • D1.2 × 10⁴

   (c)

   The tube wall must provide the force needed to keep 5.0 g of sediment moving in the circle at this radius. Calculate this force.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A car of mass 1200 kg drives round a flat, circular bend of radius 45 m. On a dry road the maximum sideways friction force the tyres can provide is 7.8 kN.

   (a)

   Calculate the maximum speed at which the car can take the bend without skidding.

   [3 marks]

   (b)

   After heavy rain the maximum friction force falls to 4.5 kN. Calculate the new maximum speed and explain what happens to a car entering the bend faster than this.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A fairground 'rotor' ride is a vertical cylinder of radius 2.5 m. Riders stand with their backs against the wall. The cylinder turns about its vertical axis at a constant 0.60 revolutions per second and the floor is then lowered. A rider has mass 60 kg.

   (a)

   A rider moves at constant speed v in a circle of radius r. Use a vector diagram of the change in velocity to derive the equation a = v²/r for the centripetal acceleration, and use it to show that a = rω².

   [6 marks]

   (b)

   Calculate the resultant force on a rider, state what provides this force, and find the factor by which the force changes if the rotation rate is doubled.

   [6 marks]

   Total for question 4: 12 marks

End of questions