Whenever you see or want to describe the effect of forces on basically any object, you'll likely be using Sir Isaac Newton's laws of motion to do it. These laws are the cornerstone of modern physics. They substantiate everything from our knowledge of planetary motion to our understanding of how planes take off and fly. This article will describe Newton's laws of motion and how they apply to everyday life.

Sir Isaac Newton

Isaac Newton was born in 1643 in England and is best known for defining the three laws of motion and universal gravitation, which laid the foundation of mechanics and modern physics. He also made breakthroughs in mathematics, inventing a new type of mathematics called 'fluxions,' or as we know it today: calculus. Before calculus, math was static, but everything is constantly moving and changing like all things in the universe. Isaac Newton's discoveries allowed engineers and mathematicians to make sense of the dynamism and motion in the changing world around us.

Law #1: all about Inertia

An object at rest remains at rest, and an object in motion remains in motion at a constant speed and in a straight line unless acted on by an unbalanced force

💡 CalcTree explainer: Things like to stay where they are; Newton's 1st law of motion describes an object's tendency to keep doing what it's doing.

Newton's first law of motion states that all objects will remain at rest or in uniform motion unless an external force changes its state. Changing the way something moves requires acceleration, and you need a net force.

An object's tendency to resist change when it's in a state of motion or stationery is known as inertia. How is inertia measured? Well, you need to know about mass. Say you throw two balls; one is a bowling ball, and the other is an inflatable ball. Intuition tells you which is harder to move or throw and harder to stop. The bowling ball has more mass; therefore, it has more inertia…more stuff to keep it doing what it's doing before you stop it.  

Newton's first law also applies to bodies at rest. Say you have an object lying on a table. The force of the object downwards onto the table due to its weight and the equivalent upward reaction exerted by the table means that all external forces cancel each other out, and the object remains at rest. In other words, there is no net force acting on the object. 

The same situation would happen if you applied equal but opposing horizontal forces on the object (provided it was on a smooth surface). Say you put two hands on an object from opposite sides and apply the same amount of pressure on each side, the external forces (from your hands) would cancel each other out, and the object will remain stationary. The object will move as soon as the forces are unbalanced (i.e., you remove one hand). Then do the same thing on a rough surface; it might be harder to slide the object across that surface because you've added another force into the mix this time. It's friction.

The concept of inertia and forces connects to Newton's second law.

Law #2: all about f=ma

The acceleration of an object depends on the object's mass, and the amount of force applied. 

💡 CalcTree Explainer: To overcome inertia, you have to apply an unbalanced or net force to an object. A 'net' force is all the forces left over after adding together all the forces that might otherwise cancel each other out. When forces get unbalanced, that's when exciting stuff happens!

The net force is found using the equation:

\begin{align*} F_{net} = m \times a \end{align*}
\begin{align*} Where,\\ m = mass\\ a = acceleration \end{align*}

You've probably heard 'force equals mass times acceleration' over and over, and for a good reason. It's likely the most used equation in physics. This equation tells us that an object that is subjected to a net external force will accelerate. The amount that an object will accelerate is directly proportional to the magnitude of the force. Acceleration is also inversely proportional to the mass of the object. This goes back to our example of two balls, one light and one heavy. If the same force is applied to both, the heavier ball will experience less acceleration than the lighter ball because it has a higher mass.

Remember: the f=ma relation is only suitable for objects that have a constant mass!

Essentially, the F= ma formula defines a force to be a change in momentum, where momentum represents the mass of an object (m) of an object times its velocity (V). But how has this simple law been derived?

Imagine a car with mass (m) with a starting velocity of (V0) starting at point X0. The car speeds up and reaches another point (X1) at a velocity of (V1). Given that the mass of the car doesn't change and that force is equal to a change in momentum with a change of time, the formula becomes:

\begin{align*} F = m \times \frac{V_1-V_0}{t_1-t_0} \end{align*}
\begin{align*} Where,\\ \frac{V_1-V_0}{t_1-t_0} = a \end{align*}

What about net force? Say you've slid a ball onto a smooth surface; your action of pushing is a force that isn't being canceled out by other forces as the ball slides forward. The ball is experiencing acceleration. All the external forces have balanced out when the ball slows down and stops moving.

The most common net force that makes an object move is gravitational force. If you throw a ball up in the air, the force of gravity pulls down on the ball once the ball loses upward momentum, and it will accelerate downwards. But gravity isn't the only force acting on an object; Newton's third law explains how to calculate net forces.

Law #3: all about forces

Whenever one object exerts a force on a second object, the second object exerts an equal and opposite force on the first.

💡 CalcTree explainer: For every action, there is an equal but opposite reaction.

Newton's third law states for every action (a force), there is an equal and opposite reaction. If object X exerts a force on object Y, Y will also exert the same but opposite force on X. If this symmetry did not exist, a chair would collapse every time you sit on it. Your body exerts a force downward onto a chair, and the chair needs to exert an equal force upwards to remain standing.

Let's quickly talk about Normal forces. A normal force is a contact force that is perpendicular to the surface that an object is on. The normal force is always perpendicular to that object, whether you rest an object on a table or on an angled ramp.

A normal force is special because it changes its magnitude. Say you have cling wrap over a deep dish and place one strawberry on it. The strawberry exerts a little bit of force onto the cling wrap; a normal force from the cling wrap pushes right back with an equal amount of force. Add another strawberry, and the force due to gravity doubles, and so does the normal force. This will keep happening until you add enough strawberries that break through the cling wrap, i.e., when the normal force cannot match the force pushing against it.

The term 'for every action there is an equal but opposite reaction,' yet this kind of symmetry needs to explain why we are indeed able to move things like picking up a cup of coffee. Well, things move because there's more going on other than just the action and reaction forces. As soon as forces become unbalanced, there's motion (refer to Law #2).

Newton’s laws Review

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Jan 19, 2023
January 19, 2023