Welcome to the World of Mechanics!
Welcome to your study notes for the Mechanics section of your Edexcel International AS Level Physics course! Mechanics is the study of how and why things move. Whether you are watching a football fly through the air or a car braking at a traffic light, you are seeing Mechanics in action.
Don't worry if some of the math seems a bit heavy at first. We are going to break everything down into small, manageable pieces. By the end of this, you’ll be able to predict the future—at least, the future of where a moving object will be!
1. Describing Motion (The SUVAT Equations)
To talk about motion, we use five variables. A great way to remember them is the acronym SUVAT:
s = Displacement (distance in a specific direction, measured in meters, \(m\))
u = Initial velocity (starting speed, in \(m/s\))
v = Final velocity (ending speed, in \(m/s\))
a = Acceleration (change in speed, in \(m/s^2\))
t = Time (in seconds, \(s\))
The Equations for Uniform Acceleration
When an object is speeding up or slowing down at a constant rate, we use these four "Golden Equations":
1. \(v = u + at\)
2. \(s = \frac{(u + v)t}{2}\)
3. \(s = ut + \frac{1}{2}at^2\)
4. \(v^2 = u^2 + 2as\)
Quick Tip: Most problems give you three pieces of information and ask for a fourth. Just find the equation that has those four variables and you are good to go!
Common Mistake: Always check your directions! If an object is moving up but gravity is pulling it down, one of those values must be negative.
Key Takeaway: SUVAT equations only work when acceleration is constant. If the acceleration changes, you can't use them!
2. Motion Graphs
Graphs are like "pictures" of motion. There are three main types you need to know:
Displacement-Time Graphs
- The Slope (Gradient) = Velocity.
- A flat horizontal line = The object is stationary (not moving).
- A straight diagonal line = Constant velocity.
Velocity-Time Graphs
- The Slope (Gradient) = Acceleration.
- The Area under the graph = Displacement (the total distance traveled).
- A flat horizontal line = Constant velocity (zero acceleration).
- A straight diagonal line = Constant acceleration.
Acceleration-Time Graphs
- The Area under the graph = Change in velocity.
Key Takeaway: If you need to find how far something went from a velocity-time graph, always calculate the area of the shapes (rectangles and triangles) under the line!
3. Scalars and Vectors
In Physics, we split measurements into two groups:
Scalars: These only have a size (magnitude). Examples: Mass, Time, Energy, Temperature, Distance, Speed.
Vectors: These have both size and direction. Examples: Force, Displacement, Velocity, Acceleration, Momentum.
Combining Vectors
If two forces are pushing in different directions, we find the resultant (the single force that does the same job as both).
- If they are at right angles, use Pythagoras' Theorem: \(a^2 + b^2 = c^2\).
- To find the angle, use trigonometry (\(tan \theta = \frac{opposite}{adjacent}\)).
Splitting (Resolving) Vectors
Sometimes a force is at an angle, and we want to know how much it pushes sideways vs. upwards. We "resolve" it into two components:
Horizontal component: \(F_x = F \cos \theta\)
Vertical component: \(F_y = F \sin \theta\)
Memory Aid: Use "Cos is Cross" (horizontal) and "Sin is Skyward" (vertical) to remember which is which when the angle is with the horizontal!
4. Projectile Motion
A projectile is anything thrown or launched (like a kicked football). The secret to solving these problems is to treat the Horizontal and Vertical motions as completely separate.
Horizontal Motion: There is no horizontal force (ignoring air resistance), so the horizontal velocity never changes. Acceleration \(a = 0\).
Vertical Motion: Gravity is pulling the object down, so it has a constant acceleration of \(g = 9.81 m/s^2\). We use SUVAT here.
Did you know? If you drop a bullet and fire one horizontally at the same time, they will both hit the ground at the same moment! This is because their vertical motion is identical regardless of their horizontal speed.
5. Newton’s Laws of Motion
Isaac Newton gave us three rules that everything in the universe follows:
First Law (Inertia): An object will stay still or keep moving at a constant speed unless a resultant force acts on it. If forces are balanced, there is no acceleration.
Second Law (\(F = ma\)): The resultant force on an object is equal to its mass multiplied by its acceleration.
\(\sum F = ma\)
Third Law (Pairs): If Object A exerts a force on Object B, Object B exerts an equal and opposite force of the same type on Object A.
Common Mistake: For Newton's Third Law, the two forces must be the same type (e.g., both gravitational) and act on different objects.
Weight and Gravity
Weight is a force caused by gravity. We calculate it using:
\(W = mg\)
Where \(g\) is the gravitational field strength (on Earth, it is \(9.81 N/kg\)).
Quick Review: Mass is the amount of "stuff" in you (measured in \(kg\)); Weight is the pull of gravity on that stuff (measured in \(N\)). Mass never changes, but Weight changes if you go to the Moon!
6. Momentum
Momentum is a measure of how hard it is to stop a moving object. We call it "mass in motion."
\(p = mv\)
(Momentum = mass \(\times\) velocity)
Conservation of Momentum
In any collision or explosion, the total momentum before = total momentum after, provided no outside forces act on the objects.
Key Takeaway: Momentum is a vector. If two objects are moving toward each other, one must have a negative velocity!
7. Moments and Equilibrium
A Moment is the turning effect of a force (like using a wrench or a see-saw).
\(Moment = Fx\)
Where \(F\) is the force and \(x\) is the perpendicular distance from the pivot.
Center of Gravity
The Center of Gravity (CoG) is the single point where the entire weight of an object appears to act. For a uniform rod, the CoG is exactly in the middle.
The Principle of Moments
For an object to be in equilibrium (balanced and not rotating):
1. The total Clockwise Moments must equal the total Anticlockwise Moments.
2. The total Resultant Force must be zero.
8. Work, Energy, and Power
Physics defines these terms very specifically:
Work Done
Work is done when a force moves an object through a distance.
\(\Delta W = F \Delta s\)
If the force is at an angle \(\theta\) to the direction of motion, use: \(\Delta W = F \Delta s \cos \theta\).
Kinetic and Potential Energy
Kinetic Energy (\(E_k\)): Energy of motion. \(E_k = \frac{1}{2}mv^2\)
Gravitational Potential Energy (\(E_{grav}\)): Energy due to height. \(\Delta E_{grav} = mg\Delta h\)
Conservation of Energy: Energy cannot be created or destroyed, only transferred. In a falling object (ignoring air resistance), the loss in \(E_{grav}\) = the gain in \(E_k\).
Power and Efficiency
Power is the rate at which work is done (how fast energy is transferred).
\(P = \frac{W}{t}\) or \(P = \frac{E}{t}\)
Measured in Watts (\(W\)).
Efficiency tells us how much energy is actually useful versus how much is wasted (usually as heat).
\(Efficiency = \frac{useful \, energy \, output}{total \, energy \, input}\)
(You can also use Power in this equation instead of Energy).
Quick Tip: Efficiency is always a number between 0 and 1 (or 0% and 100%). If you get a number higher than 1, you've accidentally flipped the fraction!
Key Takeaway: Mechanics is all about the balance of forces and the movement of energy. Master the SUVAT equations and Newton's Laws, and you have mastered the foundation of Physics!