Scalars, vectors and equilibriumAQA A-Level Physics: Subtopic test

1. 1
   A hiker walks 6.0 km due east and then 8.0 km due north, taking 2.0 hours in total, and stops.

   (a)

   What is the magnitude of the hiker's displacement from the starting point?

   [1 mark]

   • A10 km
   • B14 km
   • C7.0 km
   • D48 km

   (b)

   Which row gives the hiker's average speed and the magnitude of the hiker's average velocity?

   [1 mark]

   • Aaverage speed 5.0 km h⁻¹; magnitude of average velocity 7.0 km h⁻¹
   • Baverage speed 5.0 km h⁻¹; magnitude of average velocity 5.0 km h⁻¹
   • Caverage speed 7.0 km h⁻¹; magnitude of average velocity 7.0 km h⁻¹
   • Daverage speed 7.0 km h⁻¹; magnitude of average velocity 5.0 km h⁻¹

   (c)

   Calculate the direction of the hiker's displacement, giving your answer as an angle east of north.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A box of weight 60 N is at rest on a rough ramp that is inclined at 30° to the horizontal.

   (a)

   What is the component of the box's weight acting down the slope?

   [1 mark]

   • A30 N
   • B35 N
   • C52 N
   • D60 N

   (b)

   What is the normal contact force of the ramp on the box?

   [1 mark]

   • A30 N
   • B52 N
   • C60 N
   • D90 N

   (c)

   The ramp is raised so that it is inclined at 40° to the horizontal and the box is still at rest. Calculate the frictional force acting on the box.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A lamp of weight 30 N hangs at rest from the middle of two identical light strings. Each string is attached to a ceiling hook and makes an angle of 25° with the horizontal. The lamp and strings are in equilibrium.

   (a)

   Calculate the tension in each string.

   [3 marks]

   (b)

   The strings are pulled tighter so that each makes an angle of 10° with the horizontal. Calculate the new tension in each string, and explain why it is impossible to pull the strings completely horizontal.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A boat crosses a river that is 60 m wide with straight parallel banks. The river flows at 1.5 m s⁻¹ parallel to the banks. The boat's engine gives it a speed of 2.0 m s⁻¹ relative to the water.

   (a)

   The skipper points the boat directly across the river, at right angles to the banks. Calculate the speed of the boat relative to the bank, the time taken to cross, and the distance the boat is carried downstream.

   [6 marks]

   (b)

   The skipper now wants to reach the point directly opposite the starting point. Explain how the boat should be steered and calculate the time taken to cross.

   [6 marks]

   Total for question 4: 12 marks

End of questions