The Laws Of Newton And Forces For A-Level Maths 2023
The basis of a lot of the work covered in the Mechanics of A-Level Maths has been formed since you did some work on forces and Newton’s laws of motion in GCSE Physics or Combined Science. Therefore, in this article, we are going to place more emphasis on The Laws Of Newton And Forces For A-Level Maths to reinforce your foundation regarding Forces and Newton’s Laws for the more advanced topics.
1. What is a force?
As far as you know, a push or a pull that changes a body’s speed, direction of motion, or shape is defined as a force. A force is a push or a pull that changes a body’s speed, direction of motion, or shape. Although only simplified models are used in A-Level Maths, which means you don’t concern yourself with changes in shape, you need to be aware of the impacts of the simplifying assumptions.
It should be noted that:
- If two objects interact, each of them exerts a force on the other.
- Forces are measured in newtons (its symbol is N).
- The force which gives a mass of 1 kilogram an acceleration of 1 meter per second per second, where 1N is 1(kg*m)s‾².
- Units using negative powers – e.g. ms‾² rather than m/s²) is often written in A Level. Hence, 1 N is the force needed to make a mass of 1 kg accelerate at a rate of 1 ms‾².
Here are different types of forces and their descriptions:
- Weight: The force exerted by a body as a result of its mass combined with acceleration due to gravity. It always acts vertically downwards.
- Normal Reaction: The reaction of a surface to the weight of a body placed on it; It stops the body from falling straight through! It always acts perpendicular to the surface.
- Friction: A force that resists motion, which is caused by roughness where two surfaces are in contact.
- Air Resistance: Air’s version of friction; It resists motion and so prevents a falling object from continuing to accelerate forever.
- Tension: A pulling force in a taut string, wire or rod. It prevents two objects from moving further apart.
- Thrust: A pushing force in a rigid connector (a rod, not a string); It prevents two objects from moving closer together.
- Upthrust: A liquid’s version of friction, which acts on a body falling through it.
>>> See Also: Top 3 “Best” A-Level Maths Prep Books
2. Newton’s laws of motion
Newton’s laws of motion cover the basis of the study of statistics about forces acting between stationary bodies and dynamics regarding the relationship between forces and motion.
2.1. Newton’s first law
An object will remain at rest or continue to move uniformly in a straight line unless an external force acts on it.
In other words, the forces themselves do not cause motion; they cause changes in motion, in the form of acceleration (positive or negative). If an object is moving at a constant speed and there is no force acting on it, it will continue to move at that speed indefinitely.
However, keep in mind that it doesn’t happen in reality. For example, if you push a coin across a smooth table, it doesn’t keep happening like what is stated by Newton’s first law of motion. Because there are always moving resistances (typically air resistance and friction between surfaces) and hence deceleration ( also known as negative acceleration). In reality, no surface is completely smooth, and so whenever there are two surfaces in contact, there is an element of friction.
2.2. Newton’s second law
Although you might be given a rather wordy form of Newton’s second law, it essentially boils down to the formula F = ma, where F is the resultant force in newtons, m is mass in kilograms, and a is the rate of acceleration in ms‾².
Bear in mind that acceleration is the change in motion due to the action of a force.
2.3. Newton’s third law
For every action, there is an equal and opposite reaction.
The weight of the object is acting downwards, but there must also be a force of the same magnitude acting upwards for balance, otherwise the object will fall straight across the table. This force is called the normal reaction, usually represented in diagrams by N or R, and always acts linearly – i.e. perpendicular – to the surface.
If the forces are balanced, the system will be in equilibrium and there will be no acceleration. It does not necessarily mean no motion – see the first Newton’s law above!
If the forces are not balanced, a force will be generated and this will result in acceleration; this is where F = ma comes in.
For instance, to produce an acceleration of 5 ms‾² in an object with a mass of 6 kg, the resulting force required would be F = ma = 6× 5 = 30N.
3. Acceleration due to gravity
Your weight is the pull that the Earth exerts on you. When we look at the weight of a body, F = ma becomes W = mg, where W is the weight of the body in Newtons (we don’t measure weight in kilograms because it is mass!) and g is the acceleration due to gravity.
On Earth, g is usually between 9.8 and 9.82 ms‾² depending on where you are. Moreover, Mathematicians often use 9.8 because it is the correct rounding value for all possible values of g, though it has the disadvantage of implying that g can range from 9.75 to 9.85)
If you had a mass of 60 kg (that’s about 11 stones) your weight – on Earth – would be 60 × 9.8 = 588 N.
4. Force diagrams matching activity
Here are force diagrams, each of which labels the forces 1, 2, 3, 4, 5 using Tension, Thrust, Friction, Resistance, Weight, Normal reaction. They show the following descriptions:
A: A sledge being pulled along level ground
B: A trailer being towed by a car
C: A broom head being pushed
D: A coach being shunted (pushed) by a train engine
E: A book resting on a sloping desk lid.
F: A bead supported by a string threaded through it
G: A ladder resting up against a smooth wall
H: A plank resting on a smooth bar with one end of the plank on rough ground
In conclusion, this article has provided you with a brief overview of the Laws Of Newton And Forces For A-Level Maths. Hopefully, you’ve found it helpful. Don’t forget to prepare for your A-Level Maths with our A-Level Maths Practice Tests and look out for more future posts regarding A-level Maths content.