To undo a very tight wheel-nut on a bicycle, you need a spanner. The force you apply to the spanner has a turning effect on the nut. You couldn't undo a tight nut with your fingers but wiht the spanner you can undo it. The spanner exerts a much larger turning effect on the nut than the force you apply with your fingers to the spanner.
If you had a choice between a long-handled spanner and a short-handled one, which would you choose? The longer the spanner handle, the less force you need to exert to untighten the nut.
In this example, the turning effect of the force, called the moment of the force, can be increased by:
- Increasing the size of the force,
- using a spanner with a longer handle.
A crowbar is a lever that can be used to shift a heavy weight.
Imagine someone is trying to lift a safe with a crowbar. The weight of the safe is called the load and the force the person applies to the crowbar is called the effort. Using the crowbar. the effort needed to lift the safe is only a small fraction of it's weight. The point about which the crowbar turns is called the pivot.
You can work out the moment of a force by using this equation;
Moment = Force X Perpendicular distance from the pivot to the line of action of the force
(Nm) = (N) X (metres, M)
Centre of Mass
The design of racing cars has changed a lot since the first models. But one thing that has not changed is the need to keep the car near the ground. The weight of the car must be as low as possible. Otherwise the car would overturn when cornering at high speeds.
We think of the weight of an object as if it acts at a single point. This point is called the centre of mass ( or the centre of gravity) of the object.
The centre of the mass of an object is the point it's mass may be thought to be concentrated.
Centre Of Mass
The centre of mass of a symetrical object
For a symmetrical object, it's centre of mass is along the axis of symmetry.
If the object has more than one axis of symmetry, it's centre of mass is where the axis of symmetry meet.
- A rectangle has two axes of symmetry. The centre of mass is where the axes meet.
- An equilateral triangle has three axes of symmetry, each bisecting one of the angles of the triangle. The three axes meet at the same point, which is where the centre of the mass of the triangle is.
Q. Balance a ruler on the tip of your finger. The point of balance is at the centre of mass of the ruler. How far is the centre of mass from the middle of the ruler?
Q.Fine the centre of a mass of a semicircular card of radius 100mm.
Moments in Balance
A seesaw is an example in which clockwise moments might balance each other out.
A girl sits near the pivot to balance her younger brother at the far end of the seesaw. Her brother is not as heavy as his big sister. She sits nearer the pivot than she does. That means her anticlockwise moment about the pivot balances his clockwise moment.
The anticlockwise moment due to the weight of the sister(W1) is the clockwise moment due to the weight of the brother(W2), therefore,
Q. Use an equation to explain why the girl needs to sit nearer the pivot than her younger brother.
For an object to make equilibrium, the sum of the anticlockwise moments about any point must be equal to the sum of the clockwise moments about that point.
Look around you and see how many objects could topple over. Bottles, table lamps, and floor-standing bookcases are just a few objects that can easily topple over. Lots of objects are designed for stability so they can't topple over easily.
Imagine a tractor on a hillside. It doesn't topple over because the line of action of it's weight acts within it's wheelbase. If it's tilted more, it will topple over when the line of action of it's weight acts outside it's wheelbase. It's weight would then giave a clockwise turning effect about the lower wheel.
Q. Why is the engine of a tractor as low as possible?
- The stability of an object is increased by making it's base as wide as possible and it's centre of mass as low as possible.
- An object will tend to topple over if the line of action of it's wheel base is outside it's base.
Fairground rides whirl you around in circles and make your head spin. But you don't need to go to a fairground to see objects moving in circles.
- A vehicle on a roundabout or moving round a corner travels in a circle.
- A satellite moving across the sky moves in a circular orbit around the Earth.
- An athlete throwing a 'hammer' or a discus spins around in a circle before releasing the hammer.
For an object moving in a circle at constant speed, at any instant;
- tje object's velocity is directed along a tangent to the circle,
- it's velocity changes direction as it moves around,
- the change of velocity is towards the centre of the circle.
The object therefore accelerates continuously towards the centre of the circle. So the force on the object acts towards the centre of the circle.
What goes up most come down- unless it can overcome the force of gravty acting upon it.
The Earth exerts a force of gravity on us all. In fact, any two objects exert a force of gravitational attraction on each other. The force depends on the mass of each object. The Earth is a massive object so it'sforce of gravitational attraction on each of us keeps us on the ground.
Newton's rules on gravity
Sir Isaac Newton devised the theory of gravity over 300 years ago. He used his theory to explain why the planets orbit the Sun and why the Moon orbits the Earth. He said thatthe force of gravity between two objects;
- is an attractive force
- is bigger the greater the mass of each object is,
- is smaller the greater the distance between the two objects is.
He used his theory to make successful predictions, such as the return of comets.
On a space journey
When a sace probe moves away from the Earth towards the Moon, the force of gravity on it;
- due to the Earth decreases as it moves away from the Earth,
- dut to the Moon increases as it moves towards the Moon.
An object is heavier on Earth because the Earth's mass is much greater so it exerts a greater force on the objecton it's surface than the Moon does.
Q. What keeps the Earth moving in a circle around the Sun?
Q.Why would it be easier to launch a space probe from the Moon rather than from the Earth?
The Moon orbits the Earth in a circular orbit. The earth orbit's the Sun in an orbit that is almost circular. In general, the planets orbit the Sun in elliptical orbits which are slightly squashed circles. In each case, an object orbits a much bigger object. The centripetal forceon the orbiting object is due to the force of ravitational attraction between it and the larger object.
To stay in orbit at a particular distance, a planet must move at a particular speed around the Sun.
- If it's speed is too slow, it will spiral into the Sun
- if it's speed is too high, it will fly off it's orbit and move away from the Sun.
The further the planet is from the Sun, the less it's speed is as it moves round the Sun.
This is because the force of graavity is weaker from the Sun. So the speed of the planet needs to be less than if ti were closer to the Sun. Otherwise, the planet would fall off of it's orbit and move away from the Sun.
The further a planet is from the Sun, the longer it takes to make a complete orbit.
This is because the distance round the orbit, i.e. the circumferance, is greaterand the planet moves slower. So the time for each complete orbit (=circumference divided by speed) is longer.
Q. If the Earth's orbit were to be more elliptical, how would it be affected?
If you go to a remote area or go sailing at sea, take a GPS reciever with you. Then you will know exactly where you are. Global Positioning Satellites (GPS) send out signals that are used by areciever to pinpoint it's position. A GPS reciever fitted to a car tells a driver exactly where the car is and which direction it is going in.
Every satellite orbiting the Earth was launched into it's orbit from the groundor from aspace vehicle. Imagine launching a satellite into orbit from thetop of a very high mountain;
- If the satellite's speed is too low, it will fall to the ground,
- if it's initial speed is too great, it will fly off into space.
- At the 'correct' speed, it orbits the Earth.
For two satellites in orbits at different heights, the satellite in the higher orbit moves at a slower speed and travels further on each complete orbit. So the satellite in the higher orbit takes longer than the other satellite to complete each orbit.
The period of the satellite is the time it takes to make one complete orbit
We use satellites for communications and for monitoring.
- Communications satellites are usually in an orbit at a particular height above theequator so they have a period of 24 hours. they orbit the Earth in the same direction as the earth's spin. So they stay above the same place on the Earth's surface as they go around the earth. We describe such orbits as geostationary.
Geostationary orbits are about 36,000 kilometres above the Earth. The force of gravity there keeps a satellite moving in a circular orbit with aperiod of 24 hours.
- Monitoring satellites are fitted with TV cameras pointing to Earth. We use them for many purposes, including weather forecasting, military and police surveillance and for environmental monioring. They are in muhc lower orbits than geostationary satellites. This is so we ca see as much detail on the Earth as possible. They orbit the Earth once every two or three hours. Their orbits usually take them over the Earth's poles so they can scan the whole Earth every day.