P1: Motion

Motion

Speed, Velocity, and Acceleration

Speed is defined as the rate in which distance is travelled over time. (Formula: Average Speed = Total Distance ÷ Total Time)
Velocity is defined as the speed of an object wth a specific direction. (eg. the speed of a bicycle could be 20km/hr, but the velocity would be 20km/hr in the west direction)
Acceleration is defined as the rate of change of velocity over time (Formula: Acceleration = Change of velocity ÷ Time)
Keep in mind tht all objects fall at the same rate regardless of their mass because of gravity, all falling with the acceleration of around 9.8m/s² (excluding air resistance)

Distance-Time Graph

These graphs represent distance of an object travelling in a straight line
They show how far away the object is from the origin point over time
Time is the x-axis, Distance is the y-axis
The gradient represents the speed of the graph
The steeper the gradient, the faster the speed
When the line is horizontally flat, that means that the object is not moving over some period of time
A negative gradient means that the object is travelling back to the origin/starting point

Example of distance-time graph

Speed-Time Graph

These graphs represent the speed of the object over time
Time is the x-axis, Speed is the y-axis
The gradient represents the acceleration of the object
A line that is going upwards represents the object speeding up as it is gaining speed over time
A line going down represents the object slowing down/decelerating as it is losing speed over time
The area under the lines of the graph represent the distance travel (work this out through the formula of rectangles, triangles, and trapezoids)
A flat horizontal line means constant speed (the speed does not change)
A straight line represents constant acceleration/change in speed
Curved lines will mean fluctuating (not constant) acceleration
When the speed reaches 0, the object is at rest

Example of speed-time graph

Mass and Weight

Difference between mass and weight

Mass (normally measured in kg) is defined as the amount of matter in an object
Weight (normally measured in N) is defined as the force of gravity on mass
The formula for weight is W=mg or Weight=Mass x Gravitational Field Strength
Weights (and therefore mass) can be compared by a balance, which visually show the amount of force that gravity exerts on the object.

Gravitational field strength

Gravitational field strength is dependent on the planet, which is the source of the gravitational field strength. It is measured in N/kg which is a unit showing the amount of force applied by gravity on each kilogram of mass
The gravitational field strength on Earth is 9.8N/kg, meaning that an object with 1kg would have 9.8N of weight exerted by gravity

Density

Density is a measure of how compact a substance is, the quantity of mass per unit volume

The equation of density is ρ=m/V (in word form: Density=Mass/Volume)

The density of an object can be found depending on the state of the object

In the case that the object is a liquid, we can find the mass through weighing the liquid in a container on a balance, and determine the volume through using equipment such as measuring cylinders and observing the reading. Through finding these two pieces of information, we can substitute the values in the equation above to calculate density.
In the case that the object is a solid in a regular shape, we can find the mass through weighing the object on a balance, and determine the volume through mathematical equations (eg. the equation to find the volume of a cylinder). Through finding these two pieces of information, we can substitute the values in the equation above to calculate density.
In the case that the object is a solid that is irregularly shaped, we can use the displacement method. First, we can weigh the mass of the object on a balance. Secondly, we have to find volume. By preparing a container such as a measuring cylinder, we can fill in enough water to be able to completely submerge the object. We measure this initial volume. After that, we place the object in and make sure it is fully submerged in the liquid. We now measure the second volume. The difference of these two measured volumes would be equivalent to the volume of the object. Through finding these two pieces of information, we can substitute the values in the equation above to calculate density.

Forces

Effects of Forces

Forces can cause objects to change shape, size, or their movement. For example, in the following experiment, we can see how force can change the shape and size of a spring
There are different equations to work out force. These include...

Hooke's Law: F=kx (Force = Spring constant x Extension)
Newton's Second 2nd Law of Motion: F=ma (Force = Mass x Acceleration)

Stretching is an effect of forces

The effects of forces can be explored through the stretching of an object with a Hooke's Law experiment. The purpose of this experiment is to see how much the object stretches when a certain amount of force is applied. The steps are are follows

Before adding any mass, measuring the initial length of the spring with the ruler and note it down
After doing so, add 100g of mass (including the mass of the mass holder) and measure the length of the spring after the mass has been added
Continue this process with masses adding up to 200g, 300g... until you reach 700g and record your results in a table
After this, repeat the experiment 2 more times after removing the masses for more accurate results

Diagram of Hooke's Law experiment

Extension-load graphs

After completing your table with lengths of the spring for each value for mass in a Hooke's Law experiment, we now need to work out the extension and load/force from our raw data.
The extension can be found through this expression: Stretched Length - Original Length (the length with 0 weight)
The force can be found by multiplying the mass values found in the experiment by 9.8m/s² as objects fall at an acceleration of 9.8m/s² on Earth because of gravity
After working these values out, plot a graph with force on the y-axis and the extension on the x-axis.

You should notice that your graph should generally form a line that is mostly linear and then curves. This is because from each object has a limit of proportionality where the graph stops being linear.
The linear region will follow Hooke's Law, which was stated above, and once the line reaches the limit of proportionality, the object no longer follows Hooke's Law and will be permanently deformed even after you remove the weights.
Therefore, we can also find the spring constant from this graph by finding the slope of the linear region before the limit of proportionality. As Hooke's Law states that Force=Extension x Spring Constant, you can rearrange the equation as Force/Extension=Spring Constant. This means that the slope of the graph will equal the spring constant as well, as the slope is calculated by the formula: Change in y/Change in x. Hence, this is equivalent to Force/Extension. Based on this logic, we can find the spring extension by working out the slope of the linear region of the graph.

An extension-load graph

Friction

Friction is a force that resists an object's movement on another surface.
There is more friction on rougher surfaces
It works in the opposite direction of the object's direction and slow it down.
This force also results in heating
Air resistance is a form of friction where air acts against the movement of an object

Resultant Forces

When several forces act on an object in the same direction, the resultant force would be an addition of the two forces in the same direction (eg. a 3N force to the right and a 5N force to the right would result in a 8N force to the right)
When several forces act in opposite directions would result into movement in the direction of the force with the greater magnitude, with a force that equals to the difference between the forces (eg. a 3N fore to the left and a 5N force to the right would result in a 2N force to the right)
When several forces of equal magnitude move in opposite directions, the object will either stay stationary or continue in a constant speed. This is because there will be no change in speed, and depending on if the object was originally still or moving, one of these outcomes will be achieved

Turning effect of Forces

The moment is the turning/rotating action of an object on its axis caused by forces
A real life example of this effect is the opening of a door, where push the door, which rotates on its hinge
A moment can be calculated by the formula: Moment = Force x Distance (how long the object is from the axis to the other end)
For example, if a door was 1m and the force applied was 10N, the moment would be 10Nm
When there is no resultant force, there is no turning effect on the object, and it is said to be in equilibrium
When moments on both sides of the pivot are equal, the anticlockwise and clockwise moments are equal

For example, in this diagram, we see that...

The anti-clockwise moment is 500N x 2m = 1000Nm
The clockwise moment is 1000N x 1m= 1000Nm

As the moments are equal, the object does not have a turning effect as the clockwise and anti-clockwise moments are equal

Center of mass and pressure

The centre of mass is the point on an object where weights acts
For regular shapes, the point of symmetry is the centre of mass
For irregular shapes, an experiment can be conducted to find the centre of mass
When an object with an irregular shape is hung, the centre of mass will lie somewhere directly below it
Hang a thread from where you are hanging the object and draw the line that the thread is making on the object. Do this on two separate locations
After you have two lines, the point where they intersect will be your centre of mass

Finding the center of mass of an irregular object

Stability

In addition, the lower the centre of gravity, the more stable and unlikely topple the object
Objects with a wider base are also more stable, while those with a thinner base are less

Pressure

Pressure is worked out by Force/Area. It is often measured in the unit (N/m^2)
It is therefore defined as the amount of force applied per unit area
A real life example of pressure is that a sharper knife has less surface area and therefore applies more pressure than a duller one

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