# Forces

## contact and non-contact forces

Force is a vector, a physical quality having both direction and magnitude, measured in newtons. Other vectors include velocity, diplacement, acceleration, momentum, ect.  Vectors are shown with an arrow, the length of the arrow shows the magnitude and the direction shows the directtion of the quantity.

Some scalar quantities include speed, distance, mass, temperature, time, ect.

When two objects touch to cause a push or a full, they are contact forces. For example, friction,air resistance, tension in ropes, ect.

If the objects do not touch, they are non-contact. For example, magnetic force, gravitational force, electrostatic force, ect.

An interaction pair is a pair of forces that are equal and opposite and act on two interacting objects. For example, the sun and the earth are attracted to each other by gravitational force, which is a non-contact force, in an equal and opposite way.

Forces can change the shape of an object, the direction its going in, or its state state of rest.

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## Weight, mass and gravity

Gravity gives everything a weight and causes things on the surface of a planet to fall towards the gound. An object acted on only by gravity accellerates at about 10m/s^2.

Mass is the amount of matter an object has, it never changes. It is measured in Kg.

Weight is the force acting on the object due to the attraction of gravity and varries on location. For example a 1kg mass will weigh about 9.8N on the earth and 1.6N on the moon.

The centre of mass of an object is the point at which you can assume the mass is concentrated. For a uniform objects, this will be at the centre. When an object is suspended, it comes to an equillibriom, at rest, with its center of mass directly below the point of suspension. If the object is swung or turned it will reeturn to equillibrium.  For a flat object that is symetrical, the centre of mass is along the line of symmetry, if it has more than one it is where the axis meet.

Weight = mass x gravitational field strength

Mass and weight are directly poportional.

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## Resultant forces and work done

A resultant force is the overall force on a point or object and is found adding forces going in the dame direction and subtracting any going in the opposite direction. If the resultant force is 0, the object is either stationary or moving at a contsant speed. If two force act in the same direction the resultant force is their sum, if they act in opposite directions the resultant force is their difference.

When a force moves an object through a distance, energy is transfered and work is done on the object, either usefully or it is wasted. The thing producing the force must have a source of energy.

work done = force x distance

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## calculating forces

Scale dawings are used to find the resultant force:

1) Draw all the force acting on an object "tip to tail".

2) Draw a straight line from the start of the first force to the end of the last, this is the reultant force.

3) The lenth of the reultant force is its magnitude and the angle is the bearing.

If the reultant force is 0, the object is at equilibrium. The end of the last force will reach the begining of the first force. This will have no effect (including turing effect)

Forces with awkward angles can be split into components (resolved) by adding the horizontal and vertice components at right angles on a grid and measuring the distance between them.

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## Forces and elasticity

Hookes law

An object has been elastically deformed if it can go back to the original shape and length after the force has been removed, these are elastic objects. In this case, all the energy from the work done is transferred to the object's elastic potential energy store.

An object has been inelastically deformed if it can not go back to the original shape and length after the force has been removed. This relationship becomes non-linear.

Extension = length at stage - original length

Force = spring constant x extension           -  The sping constant depends on how stiff the object is.

The extension of a stretch elastic object is directly proportional to the load or force applied, until it reaches its limit of proportionality as long as the limit of proportionality has not been exeeded, this is non-linear.

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## Investigating springs (required practical)

Set up the apparatus as shown:

1) Clamp the ruler to the stand and measure the natural length of the spring.

2) Add a mass to the spring and record the new length of the spring. The extension is the change is length.

3) Repeat until you have at least 6 measurements.

4) Plot a force-extension graph. The force and extension should be directly proportional until it reaches its level of prooportianality. The area under the graph is the energy in the elastic potential store.

Elastic potential energy = 1/2 x spring contant x extention (until it reaches limit)

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## Distance, displacement, speed and velocity

Distance = scalar. Displacement = vector. Therfore if you walk 5m north then 5m south your diplacement is o and your distance is 10m.

Speed = how fast you're going (scalar). Velocity = speed in a given direction (vector).

Therfore you can have objects traveling at a contrant speed with a changing velocity if the direction is changing, for example a car when travelling around a roundabout).

Distance = speed x time                                        -   the average is usually given for the speed.

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## Acceleration

Acceleration is the change in velocity in a given time.It is measure in m/s^2

acceleration = change in velocity / time

Uniform acceleration is contrant acceleration. Due to gravity, objects in free fall are in uniform acceleration. They have the same acceleration as the gravitaional field strength (9.8m/s^2).

uniform accelaration:

final velocity - initial velocity = 2 x acceleration x distance   (v^2 - u^2 = 2as)

or    a = v - u / t

deacceleration is when an oject slows down, it is still the change invelocity per second.

Required practiacal: A motion sensor can show you the velocity changes of an object (toy car). This is then drawn onto a velocity-time graph and the gradient can be found. You would place a toy car at the top of a ramp and measure its veloicy as it travels down. The steeper the sloe, the higher the velocity

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## Terminal velocity

To travel at a steady spped, the diving force needs to balance the frictional force. Friction comes when two surfaces come into contact with each other or when an onject passes through water (drag). A lubricant will reduce the friction.

Air resistance is a type of drag and can be reduced by keeping the object streamline. Drag increases as speed increases.

A falling object reaches terminal velocity when the resultant force is 0, the weight of the object is then equal to the frictional force(air resistance in air, drag in water) on the object. At first the object will accelerate as gravity is more than the frictional force, however as the speed increases so does the friction.

Large, unsteamlined objects have lower terminal velocities. This is because more air resistance acts of bigger surfaces, at any given speed. This means the object will take less time accelerating until the air ressistance is equal to the accelerating force.

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## Newton's first and second laws

First law

If the resultant force on a stationary object is zero, the object will remain stationary. If the resultant force on a moving object is zero, it will carry on moving at the same velocity.

Therfore the driving forces and and resistance of moving objects at a constant speed must be balanced.

A non-zero resultant force will always produce a change in velocity in the direction of the force. On a free-body diagram the arrows will be unequal.

Second law

Force and acceleration are directly proportional. The acceleration and mass of an object are inversely proportional

Acceleration is also inversely proportinal to the mass of an object

Force = mass x acceleration

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## Inertia and Newton's third law

The tendancy to conrinue n the same state of motion is called inertia.  This changes how difficult it is to change the velocity of an object. It can be found using newtons second law                       (force = mass x acceleration), inertia is the ratio of force over acceleration.

Third law

When two objects interact, the forces they exert on each other are both equal and opposite.

Example 1) If two ice-scater were to push on each other they would feel an equal and opposite force. If both were the same mass they would accelerate in opposite directions at the same speed.

Example 2) A man pushing on a brick wall will be in equillibrium as the wall "pushes back" with equal force. This works becuase the two forces are the same type.

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## Stopping distances

Stopping distance = thinking distance + braking distance

The thinking distance is the driver's reaction time and the braking distance is the distance taken to stop under the braking force. Things that can affect the stopping distance include...

When the brake pedal in a car is pushed, brake pads push onto the wheels and cause friction and work to be done. This then transfers energy from the kinetic energy stores of the tires to the thermal energy stores of the brakes, causing a rise in temperature.

The faster a vehicle is going the more energy it has in its kinetic stores, so the more more work needs to be done to stop it. This means that a greater braking force is needed to make it stop within a certain distances.

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## Parallelogram of forces

In this diagram A and B combine to make the resulatant force, The angle between th two adjacent sides must be equal to the angle between the angles between the two forces. The resultant force is the diagonal of the parallelogram. This gemoetric method is the parallelogram of forces and must be drawn to scale to give accurate results.

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## Momentum

momentum (p) = mass (m) x velocity (v)

momentum is a vector quality and measured by kg m/s

When a collision occurs, the total momentum reamians unchanged, this is an example of the conservation of momentum and applies to any closed system (without another resultant force). Therfore the total momentum before an event is equal to the total omentum after an event in a closed system.

The greater the mass or velocity of an object, the geater its momentum.

Example:

Before a car hit another, the momementum is mass x velocity. Howvever upon a collision the mass increases but the momentum stays the same, therfore there is a dcrease in velocity.

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