Moments (Cambridge (CIE) IGCSE Physics)

A 50 cm rule is balanced at its mid-point. A force of 8.0 N acts at a distance of 10 cm from one end of the rule.

Fig. 2.1 shows the arrangement.

Calculate the moment of the 8.0 N force about the pivot. Give the unit.

moment = ............................ unit = ............................

Another force acts at a point 10 cm from the pivot. It makes the rule balance.

   On Fig. 2.1, draw an arrow to show the position and direction of this force.

A metre rule is balanced on a pivot by three vertical forces, as shown in Fig. 5.1.

Show that the moment of the 5.0 N force about the pivot is 200 N cm.

Extended tier only

Calculate the size of force F.

F = .................................................... N

Complete the statement by writing in the blank spaces.

  The moment of a force about a pivot is equal to ............ multiplied by ............

Fig. 3.1 shows a horizontal rod of length 2.4 m and weight 160 N. The weight of the rod acts at its centre. The rod is suspended by two vertical ropes X and Y. The tension in each rope is 80 N.

(i) State the name given to the point at which the weight of the rod acts.

[1]

(ii) Calculate the mass of the rod.

mass = ......................................................... [1]

(iii) The rod is in equilibrium.

  Using data from Fig. 3.1, explain why.

[4]

Fig. 2.1 shows a man pushing down on a lever to lift one end of a heavy log.

State the term used to describe the turning force exerted by the man.

(i) Fig. 2.2 shows the forces acting as the man starts to lift the heavy log.

Calculate the force F, exerted by the lever on the heavy log.

force = ..................................................... N [3]

(ii) Describe how the man can use a smaller force to lift the heavy log.

 [1] 

During a routine check of security camera footage at a zoo, it is discovered that a toucan and a grass snake have been escaping from their enclosures and performing experiments on a uniform 2 m long seesaw to study the principle of moments.

Fig. 1.1

Mass of a toucan = 600 g

Mass of a grass snake = 250 g

Calculate the weight of each animal in newtons. You may assume the acceleration of free fall is 10 m/s².

For the system in Fig. 1.1, calculate the clockwise and anticlockwise moments separately.

clockwise moment = ...................................................... N m

anticlockwise moment = ...................................................... N m

State whether the system is in equilibrium or not. Explain your reasoning.

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On a different day, the toucan and the grass snake sit in new positions at different distances from the pivot. The same 2 metre long seesaw is not in equilibrium and has a resultant clockwise moment of 5.2 N m.

A bearded dragon climbs onto on the left side of the see saw. Suggest whether it is possible for the bearded dragon to bring the seesaw into equilibrium. Explain your answer using the principle of moments.

Average weight of a bearded dragon = 4.9 N

A tower crane has a load W, as shown in Fig. 3.1.

The counterweight has a weight of 80 000 N. This acts at a distance of 5.0 m from the pivot, as shown in Fig. 3.1.

Calculate the moment of the counterweight about the pivot. Give the unit.

moment = ...........................................................

The tower crane in Fig. 3.1 balances horizontally when holding the load W. 

Calculate the weight of load W.

weight = ....................................................... N

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Fig. 2.1 shows a uniform plank AB of length 2.0 m suspended from two ropes X and Y.

The weight W of the plank is 210 N. The force in rope X is P. The force in rope Y is Q.

State, in terms of P, the moment of force P about B.

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Calculate:

(i) the moment of W about B

moment = ...........................................................[1]

(ii) the force P

force P = ...........................................................[2]

(iii) the force Q.

force Q = ...........................................................[2]

Fig. 4.1 shows a tractor fitted with a device for breaking up soil in a field.

(i) The tractor has a heavy weight at the front. Explain why the heavy weight is needed.

[1]

(ii) Fig. 4.2 represents the weight of the device and its distance from the pivot. 

Calculate the moment of the weight of the device about the pivot. State the unit.

moment = ......................................................  [4]

Fig. 4.3 shows a tractor fitted with narrow tyres and the same tractor fitted with wide tyres.

Explain why wide tyres are more suitable for the tractor on soft soil.

In a double-decker bus there are two passenger compartments, one above the other.

Fig. 3.1 shows a double-decker bus on a tilted platform.

The platform is used to test the stability of the bus.

  The angle the bus makes with the horizontal is gradually increased until the bus begins to topple to the left.

  Explain why the bus begins to topple.

There are 30 passengers in the upper compartment of a bus and 2 passengers in the bottom compartment.

  State how this affects the stability of the bus and the reason for this.

Extended tier only

A bus is travelling along a straight road. The bus and the driver have a combined mass of 16000 kg when there are no passengers in it. The bus has 73 passengers. The average mass of each of the passengers is 65 kg.

(i) Calculate the total mass of the bus, the driver and the 73 passengers.

mass = ......................................................... [2]

(ii) The fully loaded bus accelerates uniformly from rest to a speed of 14 m / s. The time taken to reach a speed of 14 m / s is 20 s.

Calculate the resultant force on the bus during the acceleration.

force = ......................................................... [2]

A university student is constructing some flat-pack furniture. 

An Allen key has a hexagonal end and is used to tighten hexagonal bolts. An Allen key can be used with its longer end in the hexagonal bolt, or can be rotated to place the shorter end in the hexagonal bolt. This is shown in Fig. 1.1.

Fig. 1.1

State which orientation, A or B, will allow the bolt to be tightened more easily. 

Explain why, referring to moments in your answer. 

The dimensions of the Allen key are shown in Fig. 1.2. 

Fig. 1.2

The student building the furniture applies a force of 150 N to the Allen key.

(i) Calculate the moment when the Allen key is in orientation A.

moment in orientation A = ...................................................... N m [4]

(ii) Calculate the moment when the Allen key is in orientation B.

moment in orientation B = ...................................................... N m [3]

The student constructs the furniture but realises they need to lift it up to place a rug underneath. 

The furniture has a weight of 800 N and is too heavy for the student to lift.

Remembering a lecture about the principle of moments, they use a pivot and a plank of wood to lift it. As shown in Fig. 1.3, the furniture exerts a perpendicular force F_A on the plank, which is equal to 30% of the weight of the furniture. 

Fig. 1.3

Calculate the minimum force F_B the student must exert to lift the furniture.

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The calculation in part (c) neglected the weight of the plank of wood.

Assuming the plank of wood has evenly distributed mass, explain how this would affect the size of the force that the student must exert to lift the furniture.