Why is a long spanner easier to use than a short one? The answer lies in the turning effect of a force.
The moment of a force about a pivot is the force multiplied by the perpendicular distance of its line of action from the pivot. Its SI unit is the newton metre (N m). For a body in equilibrium, the total clockwise moment about any point equals the total anticlockwise moment. This is the principle of moments.
A force of 10 N acts at a perpendicular distance of 0.5 m from a pivot. Find its moment.
10 × 0.5 = 5 N m
A 20 N weight hangs 30 cm to the left of the pivot of a uniform metre rule. What weight hung 20 cm to the right balances it?
Clockwise moment = anticlockwise moment, so 20 × 30 = W × 20, which gives W = 30 N
Why is it easier to push a door open near the handle than near the hinge?
The moment is force × distance from the hinge, so the same force has a bigger turning effect farther from the hinge
A couple is a pair of equal and opposite parallel forces that do not act along the same line. It turns a body without moving it as a whole, and its moment is one force multiplied by the perpendicular distance between the two forces. The centre of gravity is the point through which the whole weight of a body appears to act. A body with a low centre of gravity and a wide base is in stable equilibrium.
Two forces of 5 N each act in opposite directions 0.4 m apart. Find the moment of the couple.
5 × 0.4 = 2 N m
Why is a vehicle with a low centre of gravity and a wide base more stable?
It has to be tilted much further before its centre of gravity moves outside the base, so it is harder to topple
Give an everyday example of a couple.
Turning a steering wheel, a tap or a key, using two hands that push in opposite directions
A body moving in a circle at constant speed is still accelerating, because its direction keeps changing. The force that keeps it on the circle is the centripetal force, directed towards the centre. By Newton's law of gravitation, the force between two masses is proportional to the product of the masses and inversely proportional to the square of the distance between them. (Take g = 10 m/s².)
If the distance between two masses is doubled, how does the force between them change?
It becomes one-quarter, since the force varies as 1/r² and (1/2)² = 1/4
What provides the centripetal force for a stone whirled on a string?
The tension in the string
What provides the centripetal force that keeps the Moon in orbit around the Earth?
The gravitational pull of the Earth
1. Define the moment of a force.
2. What is the SI unit of the moment of a force?
3. State the principle of moments.
4. A force of 40 N acts at a perpendicular distance of 0.25 m from a pivot. What is its moment?
5. What is a couple?
6. Two forces of 5 N each form a couple with the forces 0.4 m apart. Find the moment of the couple.
7. What is meant by the centre of gravity of a body?
8. If the distance between two masses is tripled, what happens to the gravitational force between them?
9. In which direction does the centripetal force act?
10. What is the weight of a 45 kg boy? (g = 10 m/s²)