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Turning Effects of Forces / Moments

Notes

Momentum and Force

Momentum helps to describe how moving objects will behave.

Momentum (kgm/s) = mass (kg) × velocity (m/s)

Momentum is a vector. It has size and direction (the direction of the velocity). 


Moment

The moment of a force is the turning effect of a force, or the ability of the force to making something turn.

Moment of a force (M) about a point O is the product of the force (F) and the perpendicular distance (D) from the point to the line of action of the force.

Moment = Force x Distance

SI Unit: Newton Metre (Nm)

The turning effect of a force depends on
- location of applied force
- perpendicular distance between the point of application of the force and the pivot

Type 1,2,3 Levers



Principle of Moments

When a body is in equilibrium, the sum of clockwise moments about the balanced point is equal to the sum of anticlockwise moments about the same point (pivot).

Total clockwise moment = Total anticlockwise moment

When the clockwise moment is not equal to the anticlockwise moment, there is a resultant moment and the object will rotate in the direction of resultant moment.

If there is no resultant moment, the object is balanced.

Centre of gravity

The centre of gravity (CG) of a body is an imaginery point where the whole weight of the body seems to act in any orientation.

The CG of a regular object is at the centre.
The CG of an irregular object is determined using a plumb line.

If a body is hanging freely at rest, its CG is always vertically below the pivot, thus the plumb line method works. It can only be used for flat, irregular objects.

Stability


Stability is a measure of the body's ability to maintain its original position.

3 types of stability:

1. Stable equilibrium

Object will return to original position after slight disturbance.

2. Unstable equilibrium

Object will fall after slight disturbance

3. Neutral equilibrium

Object remains in new position after slight disturbance.


To increase the stability of a body, its base area should be increased, and the height of its centre of gravity should be decreased.

Example

A light metre rule is allowed to pivot freely at the zero end. The other end is supported by a spring balance. A weight of 200N is then hung at the 40cm mark. The metre rule stays horizontal. What is the reading on the spring balance?

Solution

By the principle of moments, taking moments about the pivot

Anticlockwise moment = Clockwise moment
F x 1m = 200N x 0.4m
F = 80N

The reading on the spring balance is 80N.

MCQ Questions

1. Which one of the following activities does not apply the turning effect of a force?
a. swinging on a swing
b. sliding down a slide
c. moving up and down on the see-saw
d. rowing a boat

2. Which one of the following quantities is zero when a uniform rod is supported in the middle?
a. mass
b. weight
c. pressure
d. moment

3. When a body is at rest, it obeys the
a. principle of momentum
b. Archimede's principle
c. principle of moments
d. principle of inertia

4. A uniform metre ruler of weight 0.2N balances at the 60-cm mark when a weight W is placed at the 80-cm mark. What is the value of W?
a. 0.1N
b. 0.15N
c. 0.2N
d. 0.2667N

5. Which one of the following measuring instruments works on the principle of moments?
a. spring balance
b. single pan beam balance
c. micrometer
d. vernier calipers

6. A uniform rod of weight 5N and length 1m is pivoted at a point 20cm from one of its ends. A weight is hung from the other end so that the rod balances horizontally. What is the value of the weight?
a. 0N
b. 0.05N
c. 5N
d. 7.5N

7. An object will not turn if the applied force on it
a. does not reach its maximum
b. does not produce a moment
c. passes through its centre of mass
d. passes through its centre of gravity

8. Levers are classified into different types according to the position of its
a. fulcrum, load and effort
b. centre of gravity
c. centre of mass
d. moment and load

9. Which one of the following statements does not describe a pair of scissors?
a. its fulcrum lies between the load and the effort
b. it is a lever of type 1
c. it works on the turning effect of a force
d. it does not have a centre of mass

10. Which of the following levers is of type 2?
a. wheelbarrow
b. scissors
c. fishing rod
d. ice tongs

11. The centre of mass of a body
a. has a fixed position
b. depends on the pull of gravity
c. is always outside the body
d. must be in a solid part of the body

12. A drinking glass has a low centre of gravity because
a. it is heavy
b. it is tall
c. it has a broad base
d. its contents are heavy

13. When a body is in neutral equilibrium, any displacement will
a. raise its centre of gravity
b. lower its centre of gravity
c. neither raise nor lower its centre of gravity
d. return the body to its original position

MCQ Answers

1. b
2. d
3. c
4. a
5. b
6. d
7. b
8. a
9. d
10. a
11. a
12. c
13. c

Structured Questions

1. A uniform metre rule AB is supported at its centre of gravity by a knife edge. A force of 5N is applied at a point which is 30cm from end A of the rule. Calculate the force which must be applied to point B to restore equilibrium.

[2.0N]

2. A boy of weight 600N sits on the see-saw as shown at a distance of 1.5m from the pivot. What is the force F required at the other end to balance the see-saw?

[450N]

3. A very light rod 40cm long is pivoted at the centre. A weight of 50N is placed at one end. Where is the place to put a weight of 200N in order that the rod is in equilibrium?

[5cm from the centre]

4. A very light rod 20cm long has weights of 60N and 40N at its ends. About which point can the rod balance horizontally?

[8cm from the 60N weight]

5. A uniform rod 1m long has masses of 100g and 40g at its ends. If it balances 30cm from one end, what is the weight of the rod?


[0.1N]

6. The figure shows a uniform metre rule pivoted at the 50cm mark. 125g and 200g weights hang from the rule as shown.

a. Calculate where you would hang a 25g mass in order to balance the rule horizontally
b. State, without calculation, how the rule with the two masses hanging as shown in the figure could be balanced without using any extra mass.


[40cm from the pivot on the side of the 200g mass]
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