MomentsAQA A-Level Maths: Subtopic test

1. 1
   A light plank is balanced horizontally on a smooth pivot. A child of mass $30$ kg sits $1.5$ m from the pivot on one side, and a second child of mass $m$ kg sits $2$ m from the pivot on the other side. Model both children as particles, with $g=9.8\ \text{m s}^{-2}$.

   (a)

   Find the moment of the weight of the $30$ kg child about the pivot.

   [1 mark]

   • A$441$ N m
   • B$45$ N m
   • C$294$ N m
   • D$588$ N m

   (b)

   Find the value of $m$.

   [1 mark]

   • A$40$
   • B$22.5$
   • C$30$
   • D$45$

   (c)

   Find the magnitude of the reaction of the pivot on the plank.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A non-uniform rod $AB$ of length $4$ m and mass $15$ kg is held horizontally in equilibrium by two vertical light strings attached at $A$ and $B$. The tension in the string at $B$ is $88.2$ N. Take $g=9.8\ \text{m s}^{-2}$.

   (a)

   Find the tension in the string at $A$.

   [1 mark]

   • A$88.2$ N
   • B$147$ N
   • C$58.8$ N
   • D$235.2$ N

   (b)

   Find the distance of the centre of mass of the rod from $A$.

   [1 mark]

   • A$2.0$ m
   • B$1.6$ m
   • C$2.67$ m
   • D$2.4$ m

   (c)

   A particle of mass $5$ kg is attached to the rod so that the tensions in the two strings are equal. Find the distance of the particle from $A$.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A uniform beam $AB$ of length $5$ m and mass $50$ kg rests horizontally on two smooth supports at $C$ and $D$, where $AC=1$ m and $DB=1$ m. A man of mass $60$ kg stands on the beam at $E$, where $EB=0.5$ m. Model the man as a particle, with $g=9.8\ \text{m s}^{-2}$.

   (a)

   Find the reaction of the support at $D$ on the beam.

   [3 marks]

   (b)

   The man leaves the beam and a child of mass $m$ kg stands at $A$. The beam is on the point of tilting about $C$. Find $m$.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A uniform diving board $AB$ of length $3$ m and mass $24$ kg is held horizontal. It is bolted down at the end $A$, so the bolt exerts a vertical downward force on the board at $A$, and it rests on a smooth support at $P$, where $AP=1$ m. A diver of mass $60$ kg stands on the board. Model the diver as a particle, with $g=9.8\ \text{m s}^{-2}$.

   (a)

   The diver stands at $B$. Find the force exerted by the bolt on the board, and the reaction of the support at $P$.

   [6 marks]

   (b)

   The bolt can withstand a force of at most $1000$ N. The diver now stands on the part of the board between $P$ and $B$. Find the greatest distance from $P$ at which the diver can stand, and state one modelling assumption made about the board.

   [6 marks]

   Total for question 4: 12 marks

End of questions