Elastic energy and the work-energy principleEdexcel A-Level Further Maths: Subtopic test

1. 1
   A light elastic string has natural length $0.8$ m and modulus of elasticity $40$ N. It is stretched so that its extension is $0.2$ m.

   (a)

   Find the tension in the string.

   [1 mark]

   • A$8$ N
   • B$10$ N
   • C$160$ N
   • D$40$ N

   (b)

   Find the elastic energy stored in the string.

   [1 mark]

   • A$2$ J
   • B$1.6$ J
   • C$1$ J
   • D$4$ J

   (c)

   The string is stretched further until its extension is $0.4$ m. Calculate the additional work done in stretching it.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A particle of mass $2$ kg is attached to one end of a light elastic string of natural length $1.5$ m and modulus of elasticity $147$ N. The other end of the string is fixed to a point $O$. Take $g=9.8$ m s$^{-2}$.

   (a)

   The particle hangs in equilibrium vertically below $O$. Find the extension of the string.

   [1 mark]

   • A$0.2$ m
   • B$0.133$ m
   • C$11.25$ m
   • D$0.4$ m

   (b)

   Find the elastic energy stored in the string when the particle hangs in equilibrium.

   [1 mark]

   • A$0.98$ J
   • B$3.92$ J
   • C$29.4$ J
   • D$1.96$ J

   (c)

   The particle is now held at rest with the string just taut, and then released. Find the speed of the particle when it passes through the equilibrium position.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A particle $P$ of mass $0.4$ kg lies on a horizontal table. It is attached to one end of a light elastic string of natural length $0.6$ m and modulus of elasticity $24$ N. The other end of the string is fixed to a point $A$ on the table. $P$ is pulled to a point $1$ m from $A$, with the string stretched, and released from rest. Take $g=9.8$ m s$^{-2}$.

   (a)

   The table is smooth. Find the speed of $P$ when the string becomes slack.

   [3 marks]

   (b)

   The table is now rough, with coefficient of friction $0.5$ between $P$ and the table. $P$ is released from rest from the same position. Find the speed of $P$ when the string becomes slack.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A light spring has natural length $0.5$ m and modulus of elasticity $40$ N. The lower end of the spring is fixed to a horizontal floor, and a ball of mass $0.4$ kg is attached to the upper end, so the spring is vertical. The ball is pushed down until the spring is compressed by $0.2$ m, and released from rest. Take $g=9.8$ m s$^{-2}$.

   (a)

   (i) Find the elastic energy stored in the spring initially.
   (ii) Find the speed of the ball when the spring first returns to its natural length.

   [6 marks]

   (b)

   Find the greatest height above its starting position reached by the ball.

   [6 marks]

   Total for question 4: 12 marks

End of questions