Mechanics: MomentsEdexcel A-Level Maths: Topic test

20 questions, 54 marks

Edexcel A-Level Maths

Mechanics: Moments topic test

Total 54 marks

Name

Class

Date

1
A uniform plank of length $4$ m and mass $10$ kg rests horizontally on a smooth pivot at its midpoint. Child $A$ of mass $24$ kg sits $1.5$ m from the pivot, and child $B$ of mass $36$ kg sits on the other side of the pivot, so that the plank is in equilibrium. Model the children as particles and take $g=9.8$ m s $^{-2}$ .
(a)
What is the magnitude of the moment of the weight of child $A$ about the pivot?
[1 mark]
A $36$ N m
B $353$ N m
C $235$ N m
D $706$ N m
(b)
How far from the pivot does child $B$ sit?
[1 mark]
A $2.25$ m
B $0.67$ m
C $1.5$ m
D $1.0$ m
(c)
Find the magnitude of the force exerted by the pivot on the plank.
[2 marks]
Total for question 1: 4 marks
2
A wheelbarrow and its load have a total mass of $60$ kg. The weight acts at a point $0.4$ m horizontally from the axle of the wheel. The gardener holds the wheelbarrow in equilibrium by applying a vertical force $L$ at the handles, which are $1.2$ m horizontally from the axle, on the same side of the axle as the weight. Model the wheelbarrow as a rigid body and take $g=9.8$ m s $^{-2}$ .
(a)
What is the magnitude of $L$ ?
[1 mark]
A $196$ N
B $235$ N
C $588$ N
D $1764$ N
(b)
What is the magnitude of the force exerted on the wheel by the ground?
[1 mark]
A $196$ N
B $588$ N
C $392$ N
D $784$ N
(c)
The load is moved so that the weight now acts $0.1$ m closer to the axle of the wheel. Find the new value of $L$ .
[2 marks]
Total for question 2: 4 marks
3
A uniform plank $PQ$ of length $5$ m and mass $16$ kg rests horizontally on two supports, one at $P$ and one at $R$ , where $PR=4$ m. A man of mass $64$ kg stands on the plank. Model the man as a particle and take $g=9.8$ m s $^{-2}$ .
(a)
The man stands at a point $2$ m from $P$ . Find the magnitude of the reaction of the support at $R$ on the plank.
[3 marks]
(b)
The man now walks towards $Q$ . Find the greatest distance from $P$ at which he can stand without the plank tipping.
[4 marks]
Total for question 3: 7 marks
4
A uniform plank $AB$ of length $4$ m and mass $20$ kg has its end $A$ on rough horizontal ground. The plank rests against a smooth horizontal rail at a point $C$ , where $AC=3$ m, and is in equilibrium in a vertical plane perpendicular to the rail, inclined at $30^\circ$ to the horizontal. Take $g=9.8$ m s $^{-2}$ .
(a)
Show that the magnitude of the force exerted on the plank by the rail is $113$ N to $3$ significant figures. Hence find the normal reaction and the frictional force at $A$ .
[6 marks]
(b)
The coefficient of friction between the plank and the ground is $0.8$ . A load of mass $M$ kg, modelled as a particle, is attached to the plank at $B$ . Given that the plank is about to slip, find the value of $M$ .
[6 marks]
Total for question 4: 12 marks
5
A mechanic turns a nut using a spanner. The force is applied at the end of the handle, which is $0.25$ m from the axis of the nut, and acts in a plane perpendicular to that axis. The mechanic applies a force of $40$ N at an angle of $60^\circ$ to the spanner.
(a)
What is the moment of the force about the axis of the nut?
[1 mark]
A $10.0$ N m
B $5.00$ N m
C $8.66$ N m
D $17.3$ N m
(b)
What is the least force, applied at the end of the handle, that would give the same moment?
[1 mark]
A $34.6$ N
B $40.0$ N
C $20.0$ N
D $46.2$ N
(c)
The mechanic slips a pipe over the handle and pushes perpendicular to the spanner at a point $0.60$ m from the axis of the nut. The nut turns when the moment is $12$ N m. Find the least force needed.
[2 marks]
Total for question 5: 4 marks
6
A uniform metre rule of mass $120$ g is marked from $0$ cm to $100$ cm. An object of mass $m$ g is hung from the $5$ cm mark, and the rule balances horizontally when it rests on a knife-edge pivot at the $30$ cm mark. Take $g=9.8$ m s $^{-2}$ .
(a)
What is the value of $m$ ?
[1 mark]
A $120$
B $150$
C $80$
D $96$
(b)
What is the magnitude of the force exerted on the rule by the pivot?
[1 mark]
A $0.216$ N
B $2.12$ N
C $1.18$ N
D $0.941$ N
(c)
The object is replaced by one of mass $150$ g hung from the same mark. The pivot is moved so that the rule balances again. Find the position of the pivot.
[2 marks]
Total for question 6: 4 marks
7
A uniform pole $AB$ of length $5$ m and mass $30$ kg has its end $A$ on rough horizontal ground. The pole is held in equilibrium in a vertical plane, inclined at $60^\circ$ to the horizontal, by a horizontal rope attached to $B$ and to a vertical post. The pole leans away from the post. Take $g=9.8$ m s $^{-2}$ .
(a)
Find the tension in the rope.
[3 marks]
(b)
Find the least possible value of the coefficient of friction between the pole and the ground.
[4 marks]
Total for question 7: 7 marks
8
A uniform barrier arm $PQ$ of length $4$ m and mass $20$ kg pivots about a smooth horizontal axis through a point $C$ , where $PC=0.5$ m. A counterweight is fixed at $P$ and may be modelled as a particle. Take $g=9.8$ m s $^{-2}$ .
(a)
The counterweight has mass $55$ kg and the arm is held horizontal by a vertical latch at $Q$ which pushes upwards on the arm. Find the force exerted by the latch and the force exerted by the pivot on the arm.
[6 marks]
(b)
The latch is removed and the counterweight is replaced by one of mass $M$ kg so that the arm balances horizontally. (i) Find $M$ . (ii) A load of mass $3$ kg is then fixed at $Q$ . Find the vertical force, applied downwards at $P$ , needed to keep the arm horizontal. (iii) Find the force exerted by the pivot in the situation in (ii).
[6 marks]
Total for question 8: 12 marks

End of questions

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).