Moments of a forceEdexcel International A Level Maths: Subtopic test

1. 1
   A light rod $AB$ of length 2 m is horizontal. A vertical force of 15 N acts downwards at $B$, and a vertical force of 24 N acts upwards at the point $C$ on the rod, where $AC=0.5$ m.

   (a)

   Find the magnitude of the moment about $A$ of the 15 N force.

   [1 mark]

   • A$30$ N m
   • B$7.5$ N m
   • C$17$ N m
   • D$15$ N m

   (b)

   Find the magnitude of the total moment about $A$ of the two forces.

   [1 mark]

   • A$42$ N m
   • B$12$ N m
   • C$30$ N m
   • D$18$ N m

   (c)

   The 24 N force is moved to a point $D$ on the rod, so that the total moment of the two forces about $A$ is zero. Find $AD$.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A uniform plank $AB$ of length 4 m and mass 30 kg rests horizontally on two supports, one at $A$ and one at $B$. Take $g=9.8$ m s$^{-2}$.

   (a)

   Find the magnitude of the force of the support on the plank at $A$ when the plank carries no load.

   [1 mark]

   • A$294$ N
   • B$73.5$ N
   • C$147$ N
   • D$30$ N

   (b)

   A man of mass 60 kg now stands on the plank at a point 1 m from $A$. Find the reaction of the support at $B$.

   [1 mark]

   • A$441$ N
   • B$294$ N
   • C$147$ N
   • D$588$ N

   (c)

   With the man still standing in that position, find the reaction of the support at $A$.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A uniform rod $AB$ of length 3 m and mass 8 kg is held in a horizontal position by two vertical light strings, one attached at $A$ and the other attached at the point $C$ on the rod, where $BC=1$ m. Take $g=9.8$ m s$^{-2}$.

   (a)

   Find the tension in the string at $A$.

   [3 marks]

   (b)

   A particle of mass $m$ kg is attached to the rod at $B$. The rod remains horizontal and the tension in the string at $A$ is now zero. Find $m$ and the tension in the string at $C$.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A uniform plank $AB$ of mass 25 kg and length 5 m rests horizontally on two supports at $C$ and $D$, where $AC=0.5$ m and $DB=1$ m. Take $g=9.8$ m s$^{-2}$ and model the plank as a rod.

   (a)

   A woman of mass 50 kg stands on the plank at a point 1.5 m from $A$. Find the reactions of the supports at $C$ and $D$.

   [6 marks]

   (b)

   The woman now walks towards $B$. Determine, with a calculation, whether she can stand at $B$ without the plank tilting.

   [6 marks]

   Total for question 4: 12 marks

End of questions