1. 1
   A technician hangs a spring vertically and adds weights one at a time, recording the load and the resulting extension each time, to investigate how the spring stretches.

   (a)

   A technician hangs a spring vertically and adds weights, staying within the limit of proportionality. A load of 6.0 N produces an extension of 0.04 m. What is the spring constant of the spring?

   [1 mark]

   • A6.04 N/m
   • B0.24 N/m
   • C150 N/m
   • D0.0067 N/m

   (b)

   The technician keeps adding weights beyond the spring's limit of proportionality. What happens to the load-extension graph beyond this point?

   [1 mark]

   • AThe spring constant increases suddenly
   • BThe graph continues as exactly the same straight line
   • CThe extension becomes zero for any further load
   • DThe graph curves, no longer forming a straight line through the origin

   (c)

   Explain what is meant by the 'limit of proportionality' and describe how the technician could identify this point from the load-extension data collected.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A stationary shipping crate on a warehouse floor has a horizontal pushing force of 200 N applied to it, but a frictional force of 200 N from the floor opposes this push, acting in the opposite direction.

   (a)

   What is the resultant force on the crate?

   [1 mark]

   • A200 N
   • B400 N
   • C0 N
   • D-200 N

   (b)

   Given that the resultant force on the crate is zero, what does this tell us about its motion, according to Newton's first law?

   [1 mark]

   • AThe crate's mass must be increasing
   • BThe crate must accelerate forwards
   • CThe crate must accelerate backwards
   • DThe crate remains at rest, since it started at rest

   (c)

   Explain, in terms of the forces acting, why the crate does not move even though a 200 N pushing force is applied to it.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A submarine moving forwards through seawater switches off its engine. Separately, a cyclist free-wheels (without pedalling) down a long hill and reaches a constant maximum speed before reaching the bottom.

   (a)

   A submarine is moving forwards through seawater when its engine is switched off. Describe the friction (drag) force acting on the submarine due to the water, and explain its effect on the submarine's motion after the engine stops.

   [3 marks]

   (b)

   A cyclist free-wheels (without pedalling) down a long, straight hill and reaches a constant maximum speed before reaching the bottom. Using the equation F = ma, explain how the resultant force on the cyclist changes as her speed increases, and why this leads to a constant maximum speed.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   An amusement park is designing a new ride. One part of the design team is testing a bungee cord (an elastic spring) for a drop tower, while another part of the team is designing a roller coaster with a full vertical circular loop.

   (a)

   Describe, in detail, an experiment to obtain a load-extension graph for a spring using slotted masses and a ruler, and explain how the resulting graph would be used to determine the spring constant of the spring and to identify its limit of proportionality.

   [6 marks]

   (b)

   A roller coaster car travels around a full vertical circular loop at constant speed. Explain, in terms of forces, why the car requires a resultant force even though its speed is not changing, describing the direction of this resultant force at the top of the loop and at the side of the loop, and relate this to why the car would travel in a straight line if this resultant force were removed.

   [6 marks]

   Total for question 4: 12 marks

End of questions