Elastic strain energyEdexcel A-Level Physics: Subtopic test

1. 1
   A spring of stiffness 250 N m⁻¹ obeys Hooke's law. It is extended by 0.060 m.

   (a)

   How much elastic strain energy is stored in the spring?

   [1 mark]

   • A0.90 J
   • B0.45 J
   • C7.5 J
   • D15 J

   (b)

   The extension of the spring is doubled to 0.120 m. How much energy is now stored?

   [1 mark]

   • A1.8 J
   • B0.90 J
   • C3.6 J
   • D1.35 J

   (c)

   The spring is attached to a trolley of mass 0.30 kg on a frictionless horizontal track. When released from this extension, all of the stored energy becomes kinetic energy of the trolley. Calculate the maximum speed of the trolley.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A metal wire obeys Hooke's law up to a force of 40 N, at which its extension is 2.0 mm.

   (a)

   What does the area under the force–extension graph for the wire represent?

   [1 mark]

   • AThe stiffness of the wire
   • BThe Young modulus of the wire
   • CThe extension per newton
   • DThe work done in stretching the wire, which is stored as elastic strain energy

   (b)

   The force on the wire is increased from 20 N to 40 N. How much more elastic strain energy is stored?

   [1 mark]

   • A0.020 J
   • B0.040 J
   • C0.030 J
   • D0.010 J

   (c)

   A student calculates the work done in stretching the wire to 40 N as 40 N × 2.0 mm = 0.080 J. Explain why this is incorrect and give the correct value.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A strip of elastic polymer is stretched within its elastic limit, and the force is measured at 2.0 mm intervals of extension. The readings are: 0 N at 0 mm, 3.0 N at 2.0 mm, 5.0 N at 4.0 mm, 6.0 N at 6.0 mm and 6.5 N at 8.0 mm. The graph of force against extension is a curve whose gradient decreases as the extension increases.

   (a)

   Estimate the elastic energy stored in the strip when its extension is 4.0 mm.

   [3 marks]

   (b)

   Estimate the additional energy stored when the extension increases from 4.0 mm to 8.0 mm. State, with a reason, whether your estimate is likely to be too large or too small.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   An archer draws a bow through a distance of 0.65 m. The draw force increases uniformly from zero to 200 N at full draw, so the bow can be treated as obeying Hooke's law. The arrow has a mass of 0.025 kg.

   (a)

   Calculate the elastic energy stored in the bow at full draw. Hence calculate the maximum speed of the arrow if all of this energy is transferred to it, and explain why the actual speed is lower.

   [6 marks]

   (b)

   A coach claims that fitting a bow twice as stiff, so that the draw force at the same draw length of 0.65 m is 400 N, would double the speed of the arrow. Assume that all of the stored energy is transferred to the arrow. Evaluate the coach's claim.

   [6 marks]

   Total for question 4: 12 marks

End of questions