Moments and equilibrium of rigid bodiesEdexcel A-Level Maths: Subtopic test

1. 1
   A uniform beam $AB$, of mass 20 kg and length 6 m, rests horizontally on two smooth supports at $A$ and at $C$, where $AC=4$ m. Take $g=9.8\ \text{m s}^{-2}$.

   (a)

   Find the magnitude of the moment of the weight of the beam about $C$.

   [1 mark]

   • A$196$ N m
   • B$588$ N m
   • C$784$ N m
   • D$98$ N m

   (b)

   Find the magnitude of the reaction at $A$.

   [1 mark]

   • A$147$ N
   • B$98$ N
   • C$49$ N
   • D$196$ N

   (c)

   A particle of mass $m$ kg is placed on the beam at $B$ and the beam is about to tilt about $C$. Find $m$.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A non-uniform rod $AB$, of length 4 m and mass 12 kg, is suspended in a horizontal position by two vertical light strings attached at $A$ and $B$. The tension in the string at $A$ is 50 N. Take $g=9.8\ \text{m s}^{-2}$.

   (a)

   Find the tension in the string at $B$.

   [1 mark]

   • A$50.0$ N
   • B$58.8$ N
   • C$117.6$ N
   • D$67.6$ N

   (b)

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

   [1 mark]

   • A$1.70$ m
   • B$2.30$ m
   • C$2.00$ m
   • D$0.575$ m

   (c)

   A particle of mass 5 kg is attached to the rod at its midpoint. Find the new tension in the string at $A$.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A uniform rod $AB$, of mass 8 kg and length 3 m, is hinged at $A$ to a vertical wall. The rod is held in equilibrium in a horizontal position by a light string attached to $B$ and to a point $C$ on the wall above $A$. The string makes an angle of $40^\circ$ with the rod. Take $g=9.8\ \text{m s}^{-2}$.

   (a)

   Find the tension in the string.

   [3 marks]

   (b)

   Find the magnitude and direction of the force exerted on the rod by the hinge at $A$.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A uniform ladder $AB$, of mass 15 kg and length 5 m, rests with end $A$ on rough horizontal ground and end $B$ against a smooth vertical wall. The ladder is in a vertical plane perpendicular to the wall and makes an angle of $60^\circ$ with the ground. Take $g=9.8\ \text{m s}^{-2}$.

   (a)

   The ladder carries no load other than its own weight and is in equilibrium. Find the magnitude of the normal reaction between the ladder and the wall, the normal reaction of the ground on the ladder and the friction force at the ground.

   [6 marks]

   (b)

   A person of mass 60 kg, modelled as a particle, climbs the ladder. The coefficient of friction between the ladder and the ground is 0.4. The ladder is on the point of slipping when the person is $x$ m from $A$ along the ladder. Find $x$.

   [6 marks]

   Total for question 4: 12 marks

End of questions