Hooke's lawEdexcel A-Level Further Maths: Subtopic test

1. 1
   A particle of mass $2$ kg is attached to one end of a light elastic string of natural length $0.8$ m and modulus of elasticity $40$ N. The other end of the string is fixed to a ceiling and the particle hangs in equilibrium. Take $g=9.8$ m s$^{-2}$.

   (a)

   Find the tension in the string.

   [1 mark]

   • A$2$ N
   • B$19.6$ N
   • C$24.5$ N
   • D$39.2$ N

   (b)

   Find the extension of the string.

   [1 mark]

   • A$0.49$ m
   • B$1.19$ m
   • C$0.392$ m
   • D$1.63$ m

   (c)

   The particle is replaced by a particle of mass $3$ kg. Find the length of the string when this particle hangs in equilibrium.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A light spring has natural length $0.6$ m and modulus of elasticity $30$ N. Take $g=9.8$ m s$^{-2}$.

   (a)

   Find the stiffness (force per metre of compression or extension) of the spring.

   [1 mark]

   • A$18$ N m$^{-1}$
   • B$0.02$ N m$^{-1}$
   • C$30$ N m$^{-1}$
   • D$50$ N m$^{-1}$

   (b)

   The spring is compressed to a length of $0.45$ m. Find the thrust in the spring.

   [1 mark]

   • A$7.5$ N
   • B$22.5$ N
   • C$4.5$ N
   • D$0$ N

   (c)

   The spring stands vertically with one end fixed to the ground. A block of mass $1.5$ kg rests in equilibrium on its upper end. Find the length of the spring.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A particle $P$ of mass $0.5$ kg is attached to one end of a light elastic string of natural length $1.2$ m and modulus of elasticity $24$ N. The other end of the string is fixed to a point $O$ on a ceiling. Take $g=9.8$ m s$^{-2}$.

   (a)

   The particle hangs in equilibrium. Find the extension of the string.

   [3 marks]

   (b)

   The particle is pulled vertically downwards until the string has length $1.8$ m, and released from rest. Find the initial acceleration of the particle.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A particle $P$ of mass $2$ kg is attached to two light elastic strings. The other ends of the strings are fixed to points $A$ and $B$, with $A$ vertically above $B$ and $AB=3$ m. String $AP$ has natural length $1$ m and modulus of elasticity $40$ N. String $BP$ has natural length $0.8$ m and modulus of elasticity $24$ N. The particle rests in equilibrium between $A$ and $B$ with both strings taut. Take $g=9.8$ m s$^{-2}$.

   (a)

   Find the extension of the string $AP$.

   [6 marks]

   (b)

   The string $BP$ is cut. Find the acceleration of $P$ immediately afterwards, stating its direction.

   [6 marks]

   Total for question 4: 12 marks

End of questions