1. 1
   A crate of mass 12.0 kg rests on a horizontal warehouse floor. The coefficient of static friction between the crate and the floor is 0.45 and the coefficient of dynamic friction is 0.30. A worker pushes the crate with a horizontal force that she increases gradually from zero. Take g = 9.81 m s⁻².

   (a)

   What is the minimum horizontal force needed to start the crate moving?

   [1 mark]

   • A5.4 N
   • B35 N
   • C53 N
   • D118 N

   (b)

   While the worker pushes with a force of 40 N, the crate does not move. What is the frictional force on the crate?

   [1 mark]

   • A0 N
   • B40 N
   • C35 N
   • D53 N

   (c)

   The worker's push reaches the value needed to start the crate moving and she then keeps it constant. Determine the acceleration of the crate once it is sliding.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A car of mass 1200 kg drives around a flat, horizontal roundabout on a circular path of radius 25 m at a constant speed of 10 m s⁻¹.

   (a)

   What is the angular velocity of the car?

   [1 mark]

   • A2.5 rad s⁻¹
   • B4.0 rad s⁻¹
   • C250 rad s⁻¹
   • D0.40 rad s⁻¹

   (b)

   Which force provides the centripetal force on the car?

   [1 mark]

   • AThe frictional force from the road on the tyres, directed towards the centre
   • BThe normal force from the road on the car
   • CAn outward centrifugal force on the car
   • DThe forward driving force from the engine

   (c)

   On a wet day the coefficient of static friction between the tyres and the road falls to 0.60. Determine the maximum speed at which the car can travel around the roundabout without skidding.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   Two gliders move on a level, frictionless air track. Glider A (mass 0.250 kg) moves at 0.60 m s⁻¹ towards glider B (mass 0.150 kg), which is at rest. After they collide, light gates record that A moves at 0.15 m s⁻¹ and B at 0.75 m s⁻¹, both in A's original direction of motion. In a second run the two gliders are held at rest with a compressed spring between them and then released; the light gates record B moving off at 0.50 m s⁻¹.

   (a)

   Show that momentum is conserved in the collision, and deduce whether the collision is elastic.

   [3 marks]

   (b)

   For the second run, determine the velocity of glider A after release, and explain how momentum and kinetic energy change during this 'explosion'.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A student measures the terminal speed of steel ball bearings falling through glycerol in a tall glass cylinder of internal diameter 4.0 cm. Steel has density 7800 kg m⁻³ and glycerol has density 1260 kg m⁻³. For a ball of radius 1.00 mm the terminal speed is 1.02 cm s⁻¹. A second ball of radius 2.00 mm, timed between two marks 10 cm apart, starting 5 cm below the surface, gives a speed of 3.2 cm s⁻¹. Take g = 9.81 m s⁻².

   (a)

   By analysing the forces on the 1.00 mm ball at terminal speed, determine the viscosity of the glycerol.

   [6 marks]

   (b)

   Evaluate whether the result for the 2.00 mm ball is consistent with the drag model Fd = 6πηrv, suggesting reasons for any discrepancy and improvements to the method.

   [6 marks]

   Total for question 4: 12 marks

End of questions