Forces & Motion

Velocity & Acceleration

Velocity

Acceleration

Magnitude - means the SIZE of a certain quantity

Speed - measured in m/s, only has magnitude but tells you nothing about direction.text

Velocity - measured in m/s, has both magnitude and direction.

Definition: the amount an object's velocity changes by in a second / the rate of change of velocity.

Acceleration (m/s2) = final v - initial v / time taken

Velocity (m/s) = distance (m) / time (s)

A big change in velocity over a short time = big acceleration.

Velocity vs Time graph

Straight slope = constant acceleration

Flat line = constant velocity

Straight slope down = constant deceleration

Gradient = acceleration

Area under line = distance

Distance vs. Time graph

Straight slope = constant forward velocity

Flat line = stationary

Straight slope down = constant velocity in the opposite direction

Gradient = velocity

Force

Weight

Terminal velocity

Resultant force

The "leftover" force, as there is often more than one force acting in opposite directions.

Force (N) = m (kg) x a (m/s2)

Definition: the force, due to gravity and mass, measure in Newtons.

An object reaches terminal velocity when the opposite forces that act upon it are equal to each other, so no resultant force.

When an object falls, it will accelerate due to gravity. However, on Earth, it does not continue to accelerate forever. The acceleration will decrease until a constant velocity.

The reason it reaches terminal velocity is because of the friction, caused by collisions with air molecules. Air resistance increases as the object falls.

Density

How to decrease terminal velocity?

Aerodynamic shape - able to cut through the air reducing air resistance, so a greater top speed can be reached.

More power - increase the power of an engine, because this means that air resistance must reach a higher value before it can balance out thrust.

Change medium - moving through a less dense medium reduces friction.

Definition: density is the ratio of an object mass to its volume.

How to find the density of an object?

Method A: Measurement. (used for object of uniform shapes such as cuboids, spheres or cylinders)

  1. Use a mass balance to find the mass in kg.
  1. Use a ruler or micrometre to calculate the volume. Apply the correct volume in m3 calculation according to its shape.
  1. Use the formula to calculate density.

Method B: Displacement (used for objects of non-uniform shape that are difficult to measure their volume)

  1. Use a mass balance to find the mass in kg.
  1. Get a displacement canister, fill it to the brim with water.
  1. Insert the object.
  1. Collect the displaced water in a measuring cylinder.
  1. Measure the volume displaced in m3.
  1. Use the formula to calculate density.

p (kg/m3) = m (kg) / V (m3)

Method C: changing volume (used for objects of non-uniform shape that are difficult to measure their volume)

  1. Use a mass balance to find the mass in kg.
  1. Fill a measuring cylinder to a known value.
  1. Insert the object.
  1. Record the increase in volume in m3 - this is your object's volume.
  1. Calculate the density using the formula.

Hooke's Law

Force

A force can change an object's direction, shape or velocity.

Stretching springs

When a force is applied to a spring or elastic band, it stretches.

If twice as much force is added, it extends twice as much.

Force is directly proportional to extension.

We do not care about length, only extension.

Do not use mass, refer as weight or force.

Graph

Limit of proportionality

Force and extension stop being directly proportional, as it is impossible to add force to an elastic band or string forever.

At this point the spring has reached its elastic limit, aka limit of proportionality.

On the graph, the line is shown to curve because an equal increase in force, length will not increase.