Force equals Mass times Acceleration

This section explains Newton's second law of motion or Force is equal to Mass times Acceleration. It is represented by F = M x A.

It is easier to understand some of these concepts if we use the European system of units. This system of units defines the unit of length as the meter. It uses the kilogram as the unit of mass. The unit of time remains the second. This system is called the MKS or meter kilogram second system. While the kilogram is not exactly the same type of unit as our pounds it may be regarded as being equal to 2.2 pounds.

Three things at once.

Before we start it is important to point out that it is hard to understand new ideas. Sometimes they need to be thought about for a while. In this section we have to learn 3 new concepts and learn to understand how all three interact with each other. This is not easy. It may take some time. In the end however it will be well worth the effort. These three new concepts are Force, Mass, and Acceleration.


Force is the thing that a elastic band exerts when is it is stretched. Other forces include the force exerted on a car by the engine and wheels. The force a person on a bicycle exerts when he pushes on the pedals. The force the wind exerts on a side of a building. The most well known of all forces is gravity. In some cases when a force is applied the object moves. In other cases ( like the wind example) the object does not move but the object is still subject to a force. Here is an example of a rather large force. It is a YouTube video of a truck tug of war. Not only is the force present in the strap between the two trucks but the driving wheels exert a force between the ground and the truck. The term Newton is used to represente force. The Newton is defined as that force necessary to accelerate a mass of 1 kilogram at 1 second per second per second


All objects have mass. A brick is an example of an object with lots of mass. A few objects (a hammer for example) rely on their mass to function. While other tools may be made out of aluminum to reduce their weight a hammer will never be. It needs it's mass to function. So let me repeat as this is important. Mass is an inherent part of any object. It does not change. Even if taken to the moon the mass of an object (or even us) does not change. The mass of an elephant is considerable but a mosquito also has mass.


Acceleration is a way of measuring a constant increase in velocity. If an object is accelerating then it is moving faster and faster. If a object has zero acceleration then it may be stopped or it may be moving at a constant speed. A dragster coming off the line is an example of an accelerating vehicle while a car moving at 60 miles per hour on the highway has zero acceleration. Likewise a parked car has zero acceleration. The best example of acceleration is to drop something to the ground. As we all know the higher it is dropped from the faster it goes and thus the harder it hits. Drop an egg from 1 inch and no problem but try 2 or 3 feet and there are different results. While velocity is measured as meters per second acceleration is measured as meters per second per second or meters / sec^2 ( meters per second squared) .

Three New Concepts

Now that these three terms have been defined we need to look at how they interact with each other. The rule of interaction is termed Newton's Second Law or Force is equal to Mass times Acceleration. For an example of F = M x A consider a rifle bullet. Before being fired the bullet is a piece of lead and is not moving. When the rifle is fired the explosion causes a quantity of gas to build up in back of the bullet. This gas exerts a force on the bullet. This force causes the bullet to move down the barrel of the gun. Now the important point. The bullet does not simply move, It is pushed by the expanding gas all the way down the gun barrel. This means it is moving faster and faster or is being accelerated. When the bullet exits the gun barrel it's acceleration stops and it begins to travels at a constant velocity. It now continues with this velocity to the target. Typical exit velocities of a rifle bullet are about 2000 feet per second or 600 meters per second. This is why a rifle bullet is more powerful than a pistol bullet. There is more time for the expanding gas to push on the bullet and this gives more time for the gas to accelerate the bullet. This leads to a higher velocity. The short barrel of a pistol limits it's time for acceleration of the bullet and thus results in a lower velocity.

How Velocity Changes

If we wish to know just how velocity changes with constant acceleration it is proportional to the time. If an object is accelerating at 2 meters per second per second then the velocity is given by V = A x T. (Velocity is equal to acceleration times the time). After 1 second the object is moving at 2 meters per second or V = 2 x 1. After 2 seconds the object is moving at 4 meters per second or V = 2 x 2. After 3 seconds the object is moving at 6 meters per second or V = 2 x 3 etc. The force of gravity causes all objects to accelerate at 9.8 meters per second.

Following there are several experiments to illustrate this point.  

Experiment 1   The Shopping Cart

Experiment 2   Illustration of F = M x A

Experiment 3  The Electric Drill

Experiment 4   Pulling a Piece of Paper out From Under a Glass of Water.

Experiment 5  A Brick on a String

Experiment 6  Dropping a Coin into an Empty Glass 

Here  is a video on Newton's 3 laws.

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