# forces

**Force, Centre of Gravity, Lever**

**Force** - a push, a pull or causes a change in the motion of an object.

If the object’s motion changes then it is accelerated.

** Forces cause acceleration. **Forces can change the speed and/or direction of an object’s motion.

Forces may also change the shape and/or size of an object.

Force (F) Unit: Newton (N)

Measuring Instrument: Newtonmeter or Spring Balance

Calculation: **Force = mass x acceleration **

* Force is in Newtons, Mass in kilograms. Acceleration in ms ^{-2.}*

A force one of one Newton gives a one kilogram mass an acceleration of one metere per second per second.

**Q**: Calculate the force required to give a car of mass 700 kg an acceleration of 3 ms^{-2}.

**Ans**: F = ma

= 700 kg x 3 ms^{-2}

= 2,100 Newtons (2,100 N)

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**Examples of Everyday Forces (Types and Effects)**

**Friction **is a contact force between the surfaces of objects restricting the movement of one across the other.

*Everyday Applications of Friction Friction in the Service of Man’*

1. Prevents sliding and slipping when walking, running

2. Nails in wood, corks in bottle, and caps on bottles.

3. Brakes on bicycles, cars, trains and planes.

4. Tying your shoes laces in a knot.

6. Parachuting – friction between air and the canopy.

7. Writing with pen, pencil and chalk.

*Friction Can be a Nuisance*

1. Increases wear & tear: brake pads, tyres.

2. Produces heat: machinery parts can become very hot

3. Produces sound: squeaky noise of chalk

4. Slows movement of cyclists, cars, trains, and planes wasting fuel to keep up speed.

**Reducing Friction **

**1. Lubricants** – materials put between the two surfaces to reduce friction.

Solid lubricants: graphite, talc, soap, grease. soap

Liquid lubricants: water, oil, synovial fluid

**2. Ball-bearings **– a layer of hardened steel balls that are free to roll between the two surfaces.

**3. Smoothing **the surfaces by filing, sanding and polishing. Streamlining

**Investigate Examples of Friction and the Effect of Lubrication**

Connect a newton-meter to a block of wood on the top of the bench. Gradually pull on the newton-meter to slowly increase the force applied to the block. Note the size of the pulling force by closely viewing the scale on the newton-meter. Record the force registered by the newton-meter just as the block begins to move. Keep a pull on the block to keep it moving slowly and steadily and record the force – note any difference!

Repeat but this time a heavy weight is placed on the block – take your measurements as before.

Repeat but this time a layer of sand paper attached to the base of the block – measure as before.

Remove the sandpaper and repeat with a layer of oil as lubrication on the table top – measure as before.

**Forces Act In Pairs**

For every force there is an equal and opposite force or *‘ for every action there is an equal and opposite reaction’.*

F_{1} = F_{2 }m_{1}a_{1} = m_{2}a_{2}

*Examples *1. Student on roller blades facing a wall and pushes the wall – student moves backwards.

2. Two students on roller blades facing each other. Who moves after a push?

3. Connect two newton-meters. Pull on one: each register the same force.

4. Firing a gun: the bullet moves forward and the gun recoils in the backward direction.

5. Deflating balloon: the balloon moves forward and the air is rushing backward.

** **

**The Force of Gravity Universal Gravitation**

A pulling force of attraction acts between all objects in the Universe, i.e. all objects in the Universe attract each other. The attractive force depends on the mass of the objects and the distance between them.

*The greater the masses the stronger the attractive force. The greater the distance the weaker the attractive force *

Gravity is the force of attraction pulling objects towards the Earth.

**What is Weight? (W) ****Unit : Newton**

The weight of an object is the measure of the force of gravity attracting it. Weight is a force and a force is measured in Newtons. Also F = ma. Force = mass (kg) x acceleration ( ms^{-2})

To calculate the weight multiply the mass of the object by the acceleration it receives in free fall on Earth.

On Earth the acceleration due to Earth’s gravity is (approx) 10 ms^{-2}. Symbol for the acceleration due to earth’s gravity: g

Therefore: Relationship Between *Mass* and *Weight* **W = mg = m x 10 ms ^{-2}**

*If the mass is known in kilograms then multiply by 10 to get the weight of the object in Newtons.*

Calculate the weight of a 40 kg student.

W = mg = mass ´ gravity

= 40 kg ´ 10 ms^{-1}

= 400 N

Calculate the mass of a school bag weighing 140 N.

W = mg

m = __W__ = __140 N__ = 14 kg

g 10 ms^{-2}

* *

**Weight Varies with Location**

1. The weigh of an object is slightly greater at the North and South poles than at the equator.

Due to the slight flattening at the poles the object is slightly closer to the centre of Earth.

2. An object’s weight is less on the top of Mt. Everest than at sea level.

The object is further away from the centre of the Earth on top of Mt. Everest.

3. An object’s weight is six times less on the Moon than on Earth.

The Earth’s gravity is six times greater than the Moon’s because of the Earth’s much greater mass.

4. In deep space very far from suns, planets and moons an object’s weight is *close* to zero due to great distances

In all four situations above **the mass** of the object **has not changed**. Remember: mass is constant (unchanging)

** **

**Extension of a Spiral Spring**

A spring is device capable of changing shape when a force acts on it and of returning to its original shape when the force is removed. **Elasticity **is the ability of a solid to recover its shape after the force is removed. Springs are used to absorb shock *(car shock absorbers ^{‘shocks’}),* store energy

*(watches)*, maintain the pressure between two surfaces and to measure force

*(Newton Balance)*. The law of elasticity,

**Hooke’s law**, “the size of the extension of the elastic object is directly proportional to the applied force.” To a certain point, the

*Limit of Elasitcity*, when the elastic restoring ability is lost forever!

**Size of deformation (extension) ÷ Force = Constant**

** **

**Investigate the Relationship Between the Extension of a Spiral Spring and the Applied Force**

Suspend a spiral spring from a clamp beside a metre rule. The spring must first be taut – so hang an object e.g. a hanger for slotted weights, from the spring. The spring is now stretched slightly and so it is taut. The spring and the metre rule must be vertical. Measure and record the position of the pointer. Now place a 1 N slotted weight on the hanger – note that the spring stretches. Measure and record the new position of the pointer and by subtracting the original position calculate the extension of the spiral spring – record this extension due to a force of 1 Newton. Repeat for 2 N, 3 N, 4 N and 5 N.

Graph the results placing force (Newtons) on the x-axis and extension (cm) on the y-axis.

Divide the extension by the load that caused that extension – the result is approximately the same for each.

*Conclusion: the extension of the spiral spring is directly proportional to the applied force.*

__ Extension__ = Constant

Applied Force

**Centre of Gravity ***of an object is the point at which its weight appears to act.*

When an object is supported at, directly below or directly above a particular point it does not fall or turn. Gravity therefore appears to act on the object at one particular point - known as the centre of gravity.

A body is in * Equilibrium * if it is not turning. If a body is not turning then it is being supported at, directly above or directly below its centre of gravity.

*Find the centre of gravity of a thin lamina (*a thin flat object)*.*

Suspend a lamina from a pin through a wide hole close to the edge of the lamina. Suspend a plumbline (string with a mass at the end) from the pin across the front of the lamina. The lamina is in equilibrium and so the point of support is directly above its centre of gravity. The plumbline shows the vertical from the point of support.

The centre of gravity is somewhere along this vertical line. Mark the position of the plumbline at the far edge of the lamina. Place the lamina on the table top and draw a straight line from the point of support (the pin hole) to the mark. The centre of gravity of the lamina is somewhere along this line. Repeat the procedure twice more from two other points of support. The point at which these three ‘vertical’ lines meet is the centre of gravity of the lamina. Support the lamina at this point – it does not fall or turn.

* Stability *is a measure of how difficult it is to move an object from its equilibrium position

i.e. how difficult it is to get the object to turn or topple over.

The stability of an object can be improved by a) Widening its support base.

b) Lowering its centre of gravity.

*Stability Design in Everyday Objects *

a) Wide Support Base 1. Stabilisers on a child’s first bicycle.

2. Reading lamp base. 3. Widely spaced rear wheels of a tractor.

b) Low Centre of Gravity – *usually by having a lot of ‘weight’ close to the base.*

1. Infant’s drinking cup.

2. A whiskey glass – a very thick base of glass.

3. The chassis of a bus. (engine at the bottom)

c) WideBase and a Low Centre of Gravity 1. A racing car.

2. A traffic cone.

**Levers**

A lever is a rigid object that is free to turn about a fixed point or line of support called the fulcrum.

A lever is an example of a simple machine and is designed to allow work to be done more conveniently.

*Everyday Applications of Levers*

Spanner to turn nuts. Scissors Forceps (Tweezers) Bottle opener. Door handle Crowbar

Oar Bicycle handle bars Our moveable bones.

**The Turning Effect of a Force**

Hold a metre-rule horizontal and suspend a weight from the metre-rule beside your hand Gradually have the weight (force) moved out along the metre rule from your hand. You experience an increasing turning effect.

Repeat with heavier weights. Conclusion: the turning effect increases with distance and increasing weight.

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** **

**Moment of a Force **is the turning effect of a force and is calculated by multiplying the size of the force by the distance form the point of action of the force to the fulcrum. Moment = Force ´ Distance

**Law Of The Lever ***‘principle of moments’*

When a lever is in equilibrium i.e. balanced, the sum of the clockwise moments is equal to the sum of the anticlockwise moments.

*Investigating the Law of the Lever*

The metre rule is uniform – its centre of gravity is at the 50 cm mark. Suspend the uniform metre-rule at the 50 cm mark. Hang a 3 N weight on the left of the fulcrum and a 2 N weight on the right. Move the two weights until the metre rule lever is balanced.

Record the positions of the two weights and calculate their distance from the fulcrum – the 3 N is at the 30 cm mark and the 2 N is at the 80 cm mark. The metre-rule is in equilibrium – it is balanced, it is not turning.

Calculate the anticlockwise moment and the clockwise moment.

Now hang two weights on the left of fulcrum and two on the right until the metre rule is balanced.

Left side of fulcrum: 1 N at the 10 cm mark and 5 N at the 30 cm mark.

Right side of fulcrum: 3 N at the 70 cm mark and 2 N at the 90 cm mark.

Calculate the sum of the anticlockwise moment and the sum of clockwise moments.

**Pressure **is the force per unit area. *Pressure = Force *Unit: Pascal Pascal Symbol: Pa

* Area *1 pascal is a force of 1 newton per square metre.

In some situations a high concentrated force is useful so a small area of contact is desirable e.g. scissors, knife

In others low pressure is better and so a large area of contact is in the design e.g. wide tyres, school bag straps,

*2 Factors Affecting Pressure *1. the size of the force – the greater the force the greater the pressure.

2. the area of contact – the smaller the area the greater the pressure.

*Simple Pressure Calculations*

Calculate the pressure of the block on a table top. A 300 N block with one side of 6 m^{2} and another side of 15 m^{2} Dimensions of the rectangular block: 2 m, 3 m and 5 m.