Forces

Contact and non-contact forces

• A force is a push or pull that acts on an object due to its interaction with another object

  • Force is a vector quantity, and is measured in newtons

• A contact force is when two objects are physically touching

  • Friction, air resistance, tension and normal contact force

  • Normal contact force (reaction force) is the idea that there is an equal and opposite force from an object opposing its weight

• A non-contact force doesn’t require objects to be touching, and has fields of influence

  • Gravitational, magnetic and electrostatic

  • The strength of the force depends on the distance from the object

Scalar and vector quantities

• Scalars are physical quantities that only have a magnitude (size)

  • Speed, distance, mass, temperature, time, etc.

• Vectors have both magnitude and direction

  • Velocity, displacement, acceleration, force, momentum, etc.

  • Arrows represent the direction of the force, and the size of the arrow represents the magnitude

    • Can be negative (-4km east = 4km west)

Free body diagrams and resultant force

• Resultant force is the overall force and it direction that is acting on an object

• Equilibrium is when there is no overall resultant force on an object (either stationary or travelling at a constant speed)

Elasticity, spring constant and Hooke’s law

• When a force is applied to an object, it compresses, stretches or bends

  

  • More than one force has to be applied for an object to stay stationary

• Elastic deformation is the idea that after a force has been applied to an object, it returns to its original shape

• Inelastic deformation (plastic deformation) is the idea that after a force has been applied to an object, the object doesn’t return to its original shape

• Extension is the increase in length of a spring when stretched 

• The spring at its natural length has no force acting on it, but when a weight is added it extends

  • There is still a normal force acting opposite from the support

  • As we increase the force, the extension increases proportionally as long as the limit of proportionality isn’t reached - Hooke’s law

• F∝e or F=ke

  • Force is directly proportionate to extension, and is dependent on the spring constant of the object

• Spring constant is how many newtons it would take to stretch an object by 1m

• Once the limit of proportionality/elastic limit is reached, Hooke’s law no longer applies, an inelastic deformation has occurred 

Elastic potential energy

• F=ke

  • K is spring constant, and a lower spring constant means higher elasticity

• Ee=½ke² 

  • Elastic potential energy is the energy transferred to an object that is stretched 

• Area under a force/extension graph is equal to the energy transferred, and the gradient of the straight line, where Hooke’s law applies, is equal to the spring constant

Moments

• A moment is the rotational or turning effect of a force

• M=Fd

  • Moment (Nm) = Force (N) x distance (m)

  • A larger distance and greater force creates a greater moment 

• When there is more than one moment, there is both an anticlockwise moment and a clockwise moment

• There’s an anticlockwise moment on the left and a clockwise moment around the right

  • If the clockwise moment equals the anticlockwise moment, there is no overall moment

  • Different distance can balance different weights (force) 

• Levers transmit the turning effect of a force

  • The input force transmits to the output force

  • If the forces are on  opposites sides of a pivot, they will act in different directions

  • If the forces are both on the same side of the pivot, they will act in the same direction

  • The output force is generally closer to the pivot, so it is able to create a larger output force with a small input force

• Gears transmit turning effects

• A is connected to an engine and turns clockwise, which causes B to rotate anticlockwise

  • Gears turn in opposite directions

  • Different sizes of gears change the size of the turning effect/moment

    • A has a larger radius, so a larger turning force

  • B turns faster than A as it has a small radius

  • The overall work done on each side is equal as B turns faster than A, which is balanced by A having a greater turning effect/moment 

    • The ratio of the turning effect of the two gears is proportional to the ratio of the radius of the two gears

Pressure

• Pressure is the force per unit of area

• P=F/a

  • Pressure (Pa) = Force (N) / area (m)

• Pressure in a fluid is creates by collisions between particles and surroundings

  • In gases, particles collide with a wall and other particles, which creates pressure (a force applied to an area)

  • In liquids, particles collide with walls and the air at the surface

• Pressure in a solid is created by collisions between two solid objects

• We aways use the perpendicular force 

  • The component that is at right angles to the surface its colliding with

• If it is at a right angle, the entire force will generate pressure on the wall

  • If it is at an angle, only a small part of the force will generate pressure as the force is split into two parts, and only one collides with the wall

Liquid pressure and upthrust

• Pressure in liquids

  • The deeper an object, the greater the weight of the water, so there is higher pressure

  • The density of the liquid depends on the number of particles - denser = more pressure, as more particles colliding with the object

  • Gravitational field strength also impacts the pressure of liquids - a larger gravitational field strength, a larger weight (gfs x mass), so higher pressure

  • P=h$\rho$ g

    • Pressure (Pa) = depth (m) x density (kg/m³) x gravitational field strength (N/kg)

• Whether an object sinks or floats, depends on the pressure

  • The bottom of an object is deeper than the top, so there is a larger upwards force that downward force

    

  • This creates a resultant force upwards (upthrust)

• All submerged items have upthrust, so whether they float or sink depends on their weight (downward force)

  • If the upthrust is greater than the weight, it floats

  • If the weight is greater than the upthrust, it sinks

• If an object is more dense than the liquid, it sinks

Atmospheric pressure

• The closer to the surface, the higher the pressure as there are more particles creating weight, as well as more collisions with the surface creating pressure

  • At sea level, there are all the particles above it, which creates weight and therefore pressure

Speed, velocity, distance and displacement

• Speed is a scalar quantity

  • For example, 4 m/s

• Velocity is a vector quantity

  • For example, 6 m/s east

• Distance is a scalar quantity

  • For example, 10m

• Displacement is a vector quantity

  • For example, 40m east

• Speed = distance/time, so no direction

• Velocity = displacement/time, so has direction

• Real life speeds

  • 1.5m/s - walking

  • 3m/s - running

  • 6m/s - cycling

  • 25m/s - cars

  • 55m/s - trains

  • 250m/s - planes

  • 330m/s - sound waves in air

  • 0 → 55m/s - wind (affected by temp, pressure and structures)

Acceleration

• Acceleration is the rate of change of velocity

• a = △v/t

  • Acceleration(m/s²) = change in velocity(m/s) / time(s)

  • It shows average velocity over time

  • A vector quantity, so can be negative

• 2as = v² - u²

  • 2 X acceleration x distance = final velocity squared - initial velocity squared

  • Initial velocity is 0 if from stationary

Distance/time graphs

• Distance/time graphs are used to represent the distance travelled over time

• Gradient = speed (d/t)

• A shows a constant speed

  • B shows where the object is stationary

  • C shows an increase in speed, so the object has accelerated

• To find a speed at a specific point, use a tangent of a line

Velocity/time graphs

• Velocity/time graphs show speed at any time

• The area under the graph equals the total distance travelled over time (m/s x s = m)

  • For curved sections, estimate the number of squares covered

• The gradient equals acceleration

Terminal velocity

• Terminal velocity is the point where a falling objects reaches a constant speed, with no acceleration

• At first, there is a split second when an object is stationary before it begins to fall

  • The object has mass, and is in a gravitational field so experiences a downwards force of weight

  • This is the only force that acts, so the resultant force is down and the object begins to fall, accelerating downwards

• The object continues to accelerate, but as it continues to fall it begins to experience air resistance

  • This is an opposite force to weight, so lowers the resultant force downward

  • The object still falls, but it’s acceleration decreases

• Air resistance is due to the air particles colliding with the person , so slows them down

  • The size of air resistance depends on the surface area and their velocity (faster = more collisions)

• As they continue to fall, the air resistance increases due to the higher velocity

  • The resultant force downwards is much smaller

• Eventually, the air resistance will balance out the weight and the resultant force will be 0

• Here the velocity no longer changes - terminal velocity has been reached

• If they open their parachute, the surface area increases so air resistance is higher

  • They will decelerate until resultant force becomes 0 again

  • A new terminal velocity has been reached, that was lower than before

Newton’s first and second law

• Newton’s first law says that a resultant force is required to change the motion of an object

  • It will continue at a constant speed or remain stationary unless there is another force

• Newton’s second law says that if an object has a resultant force acting on it, the object will accelerate until the forces acting change

  • If it was stationary, it starts to move

  • If it was moving, and the force acts in that same direction, it will speed up

  • If it was moving, and the force acts in the opposite direction, it would slow down or stop before changing direction

  • It could result in a change in direction without a change in speed

    • Change in velocity / change in time = acceleration, so only direction has to change

    • Like with orbits (la moon…)

    • Called circular motion

    • Direction is always changing as the gravitational pull acts perpendicular to the moon’s motion and speed is constant - acceleration

• Newton’s second law also states that the size of the resultant force is directly proportional to the acceleration it causes

  • F=ma, so if mass is constant F$\alpha$a

• Inertia is the tendency for the motion of an object to remain unchanged

  • Basically Newton’s 1st law - stationary or constant unless another force

• Inertial mass is how difficult it is to change an object’s velocity

  • Inertial mass = force / acceleration (F=ma)

  • A large mass would require a larger force to change it’s velocity (small acceleration)

Newton’s third law

• Newton’s third law says when two different objects interact, the forces they exert on each other are equal (magnitude) and opposite (direction)

  • If there was a box and a person pushing it, either the box could move or the person could (bounce back)

    • If the box has a lower mass, it would move

    • If the box was heavier, the person would be pushed back

    • If the box was medium mass, the person would be pushed back and the box would move forward

• F=ma → a=F/m - for an object to accelerate and move, there needs to be a high force or small mass

Stopping distances

• Stopping distance is the minimum distance required to stop a vehicle in an emergency

  • Stopping distance = thinking distance + braking distance

• Thinking distance is how far the car travels during the driver’s reaction time

  • Between seeing the hazard and starting to brake

  • This depends on speed and reaction times

  • Faster speed equals longer distance

  • Reaction times depend on tiredness, drunkenness, drugs and distractions present

• Braking distance is the distance taken to stop under a braking force

  • This depends on speed, mass, condition of brakes and traction

  • Condition of brakes - if they are worn or faulty, they won’t slow the car and it will travel further

  • Traction is affected by ice/wet (less friction) and bald tires (can’t grip road), so the car travels further

• Thinking distance increases proportionally with speed

• Braking distances increases more the faster it is

  • Speed x2 = time x4

  • Speed x3 = time x9

Momentum

• $\rho$ = m x v

  • Momentum(kgm/s) = mass(kg) x velocity(m/s)

• Momentum is a measure of how difficult it is to stop a moving object

  • A vector quantity (has direction)

• Conversation of momentum says that in a closed system, the total momentum before an event is equal to the total momentum after an event

• If a gun was fired from stationary, momentum would have to be 0 after

  • The gun moves back - recoil

• If a force is applied to a moving object, it accelerates, so its momentum is increased

  • The force applied can be calculated with force = change in momentum/time

  • A greater time equals a lower force, so less damage

• This is why cars’ safety features increase the time taken for impact or decrease speed, therefore decreasing force

  • Crumple zones, seat belts (slightly stretchy so slower) and air bags (more time, so lower momentum)

DONE!!