# Forces

- Created by: holly6901
- Created on: 13-06-19 12:00

## Velocity vs speed

Speed

- Speed is a scalar quantity.
- Scalar quantities only have a magnitude (size).
- Scalar quantities, like speed, do not have a direction.

Velocity

- Velocity describes an object’s direction as well as its speed.
- Velocity is a vector quantity because it has a magnitude (or size) and a direction.

## Vectors

To add vectors, draw each vector as an arrow one after the other.

- The length of the arrow represents the magnitude (size) of a quantity.
- The direction of the arrow represents the direction of the vector quantity.
- Jane pushes a table with a force of 10N towards the door, but her brother, Frank tries to stop her by pushing it with a force of 10 N at a right angle to Jane.
- The effect of these forces is shown above.
- Pythagoras’ theroem is used to work out the resultant force.
- Resultant Force = √(102 + 102) = √(200) = 14.1 N.

## Velocity

If two people stand back-to-back and walk away from each other at the same speed, but in opposite directions, their speeds are the same but one will have positive velocity and the other will have negative velocity.

## Distance vs displacement

Distance

- Distance is how far an object moves.
- Distance is a scalar quantity.
- This is because it contains a magnitude (size) but not a direction.

Displacement

- Displacement is the distance an object moves in a straight line from a starting point to a finishing point.
- Displacement is a vector quantity.
- This is because it contains a magnitude (size) and direction.

## Contact and non-contact forces

Non-contact forces

Non-contact forces happen when objects are separated (not touching).

- Gravitational force, electrostatic force and magnetic force are all examples of non-contact forces.

Contact forces

Contact forces happen when two objects are physically touching.

- Friction, air resistance, tension and normal contact force are all examples of contact forces.

## Contact forces

- Friction comes about whenever two surfaces are touching and try to move against each other.
- Tiny bumps in the surface interlock (overlap or fit together). This creates a frictional force that opposes their motion.
- Air resistance comes about when an object moves through the air and collides with (hits) air molecules.
- This creates a force that slows the object down.
- Tension is the pulling force that a string or cable exerts (creates) when something or someone pulls on it.
- When you push on a table, your hand doesn't move through it.
- This is because the normal contact force from the table pushes equally on your hand.

## Distance time graphs

Distance-time graphs have distance on the y-axis and time on the x-axis.

- On a distance-time graph, motion (movement) at a constant speed is shown by a straight line.
- If the line is horizontal, then the object is stationary.

## Speed time graphs

Speed-time graphs have speed on the y-axis and time on the x-axis. Velocity-time graphs would simply have velocity on the y-axis instead of speed.

- If an object’s speed is constant, then the speed-time graph will be horizontal.
- If the object is not moving (is at rest), the graph will run along the x-axis because that is where y = 0.
- Acceleration determines the change in speed.
- If the speed of an object increases with time, its graph will have a positive gradient.
- If an object slows down, its graph will have a negative gradient.

## Speed time graphs

- A straight line on a speed-time graph shows that acceleration is constant. If the line is horizontal the acceleration is zero.
- If the line is curved, it shows that the acceleration was not constant.
- Holding your ruler next to a curve (at a tangent) can allow you to see whether acceleration is increasing or decreasing.
- If the line of your ruler gets steeper, then the acceleration is increasing.

## Distance time graphs

- If an object’s speed increases, the object will travel a longer distance in the same amount of time.
- The slope (gradient) of the distance-time graph will become steeper.
- If an object’s speed decreases, then the object will travel a shorter distance in the same amount of time.
- The slope (gradient) of the distance-time graph will become less steep

## Mass

Mass

- An object's mass is a measure of the amount of matter that it contains.

Centre of mass

- Although the mass of an object is spread out across its body, it is possible to find a single point where all of the mass appears to be. This point is called the object’s centre of mass.
- If an object is hung from a string, it will hang with its centre of mass directly below the point that it is hung from.
- An object will fall over if its centre of mass is outside its base.
- An object will fall off a surface if its centre of mass isn’t over the surface.
- The centre of mass is the point through which an object’s weight appears to act.

## Force and acceleration

- The resultant force is the sum of all of the forces acting on an object.
- The change in an object’s motion is caused by the resultant force.
- If the forces acting on an object are unbalanced (not equal) it means that a resultant force is acting on the object.
- A resultant force causes an acceleration.
- The acceleration can be calculated with this equation.
- Resultant force (F) = mass (m) x acceleration (a).
- This is Newton's 2nd Law.

## Newton's 1st law

- If an object is stationary (not moving) and there is no resultant force acting on it, it will stay stationary.
- If an object is moving and there is no resultant force acting on it, the object will continue moving in the same direction at the same speed.
- This means that the object will continue moving at the same velocity.
- This also means that the velocity of an object will only change if a resultant force is acting on the object.

## Newton's 3rd law

- Newton’s Third Law says that: whenever 2 objects interact, the forces that they exert on (apply to) each other are equal and opposite.
- If one object exerts (applies) a force on another object, then the other object must be exerting (applying) a force back.
- If a hand pushes on a table, the table will push back on the hand with an equal force, but in the opposite direction.

## Newton's 3rd law

- Newton’s Third Law says that: whenever 2 objects interact, the forces that they exert on (apply to) each other are equal and opposite.
- If one object exerts (applies) a force on another object, then the other object must be exerting (applying) a force back.
- If a hand pushes on a table, the table will push back on the hand with an equal force, but in the opposite direction.

## Stretching, bending and compressing

- We can stretch, bend or compress objects by applying forces to them.
- For this to happen, there must be 2 or more forces acting on an object.
- If only one force is acting, the object will just move in the direction of that force.
- Because of this, we can normally only stretch, bend or compress stationary (still) objects.

## Elastic and inelastic deformation

Inelastic deformation

- An inelastically deformed object will not return to its original shape when the force stops.
- A car is an inelastic object.
- After a car has crashed into a tree, it will not return to its original shape.

Elastic deformation

- An elastically deformed object will return to its original shape when the force stops.
- A spring is an elastic object.
- Springs return to their original shape when forces stop acting on them.

## Extension-load graphs

- An extension-load graph has the force acting on a spring plotted on the y-axis, and the extension of the spring on the x-axis.
- For low forces the graph is a straight line which passes through the origin.
- When no force acts on the spring, there is no extension.

- As the force on the spring increases, the spring reaches its limit of proportionality.
- On the graph above, this is where the line begins to curve.

## Hooke's Law

- When a spring is stretched, the increase in the length of the spring is called its “extension”.
- Hooke’s Law tells us that the extension of a spring is directly proportional to the force applied to the spring:

force = spring constant x extension. - Think of the spring constant as the stiffness of the spring. This is different for different objects.
- The higher the spring constant, the “stiffer” the spring and the more force is needed to stretch it.
- The limit of proportionality is the point where Hooke’s law breaks down.
- If a spring is stretched too much, it will not return to its original length when the force stops acting on the spring.

## Work done on a spring

Work done on a spring

- When we compress a spring, elastic potential energy is stored in the spring (so long as a spring isn’t inelastically deformed!).
- The elastic potential energy stored in a spring is equal to the work done when stretching it.

Elastic potential energy

- The elastic potential energy stored in a stretched spring equals the area under the force-extension graph.

## Free fall and air resistance

Free fall

- An object in free fall will accelerate at a constant rate. This constant rate is called the acceleration due to gravity (g).
- The average value for acceleration on Earth due to gravity is 9.81 m/s2, but we round it up to 10 m/s2 in most calculations.

Air resistance

- Air resistance is a frictional force that opposes the motion of objects moving quickly through air.
- Air resistance slows down a falling object.

## Terminal velocity

Terminal velocity

- The force due to air resistance increases as the speed of a falling object increases.
- Once the weight force and force due to air resistance are equal, the object stops accelerating - it has reached terminal velocity.
- The terminal velocity is the fastest the object can fall.
- Near the surface of the Earth, objects falling freely under gravity accelerate at about 9.8m/s2.

Free fall - graphs

- The speed-time graph for the object is a straight line with a constant slope, showing that the object’s acceleration is constant.
- The slope of the speed-time graph has a value equal to g (the object’s acceleration due to gravity).

## Stopping distance

Stopping distance

- The time it takes for a driver to react to a situation is their reaction time.
- During this reaction time, the car carries on moving.
- The thinking distance is the distance travelled between when the driver realises they need to brake and when they apply the brakes.
- The distance the car travels between the driver applying the brakes and the car stopping.

Factors affecting thinking distance

- Distraction i.e. phones , small children
- Tiredness
- Drugs or alcohol

## Braking distance

Factors affecting braking distance

- Condition of the car
- Road conditiions
- Initial car speed

Work done when braking

The greater the speed of a vehicle, the greater the braking force needed to stop the vehicle in a certain distance.

- This means that more work needs to be done on the brakes to stop the car
- The greater the mass of the vehicle, the greater the braking force needed to stop the vehicle. This means that more work needs to be done on the brakes to stop the car.
- For the same work done, the stopping distance will decrease if the force (grip) between the road and the vehicle increases.

## Dangers of large decelerations

- When a typical family car decelerates at a set of traffic lights, only a small force is exerted on (applied to) the passengers.
- This is because the deceleration happens over a long period of time.
- The force doesn't harm the passengers.
- When a typical family car suddenly stops in the road to avoid a collision, a greater force is exerted on (applied to) the passengers.
- This is because the deceleration happens over a shorter period of time.
- The force should not be enough to harm the passengers.
- When a typical family suddenly is stopped by a crash, an even greater force is applied to the passengers than the last example.
- This is because the deceleration happens in even less time.
- This could harm passengers.

## Force and momentum

A car of mass 500kg comes to a stop from an initial speed of 2m/s in a time of 4s.

- Change in momentum = m(v − u) = 500 × (2 − 0) = 1000kgm/s.
- Force = change in momentum ÷ time taken.
- Force = 1000 ÷ 4 = 250N.

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