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Newton's Second Law of Motion

The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.

F = m * a

F: force exerted,
m: mass of the object,
a: acceleration produced as a result.

Acceleration is simply the rate of change of velocity, that means by 'how much' will the velocity of the object increase or decrease per unit time.

EXPERIMENT 1

To understand this law, we will examine the effect of force and mass on acceleration individually. First, lets keep a constant mass of 10kg and vary the force.

Move the slider to assign a new value to force and click on "ROLL". Try this with 2-3 different values of force, then observe the graph.

Move the slider to choose a 'Force' value and click on 'Roll'




ANALYSIS

Did you notice the change in the ball's speed as you increased the force? If you notice that the ball moved faster, then you're right! This kind of relation between two variables is called "Direct Proportion". This means, as one increases, the other variable also increases.

Now look at the graph, how does it look? Does it look like the graph here, a straight line at an angle of about 45 degrees? If it doesn't, why don't you try out a few more values of force? Acc vs Force

Linear Dependency Graph

This kind of relationship is called "Linear Dependency". This means as one variable increases, the other by the same factor irrepective of the value of either variable. That means, in this case, whether force is 500N or 2500N, acceleration will increase by same factor of 0.1 (for a constant mass of 10Kg)

To understand this law, we will examine the effect of force and mass on acceleration individually. First, lets keep a constant mass of 10kg and vary the force.

Move the slider to assign a new value to force and click on "ROLL". Try this with 2-3 different values of force, then observe the graph.

EXPERIMENT 2

Now, lets keep a constant force of 2500N and vary the mass.

Move the slider to assign a new value to mass and click on "ROLL". Try this with 2-3 different values of mass, then observe the graph.

Move the slider to choose a 'Mass' value and click on 'Roll'




ANALYSIS

This time, did you anything different in how the ball's speed changed as you increased the mass? Now, the ball moved slower as you increased the mass. This kind of relation between two variables is called "Inverse Proportion". This means, as one increases, the other variable decreases.

Now look at the graph, how does it look? Does it look like the graph here, a curve in the shape of a slide? If it doesn't, why don't you try out a few more values of mass? Acc vs Force

Reciprocal Dependency Graph

This kind of relationship is called "Reciprocal Dependency". This means as the independent variable changes, the dependent variable changes by an exponential factor that depends on the value of the independent variable. That means, in this case, as you move from mass 10Kg to 100Kg the change in acceleration will slow down (for a constant force of 2500N)

SUMMARY AND QUICK TEST

To summarize, Newton's second law of motion basically means that acceleration is affected by both the force exerted and the mass of the object. The more force exerted, the more acceleration is produced. The more mass the object has, the lesser acceleration is produced. Thus force and mass kind of balance each other.

Now lets see if you've fully understood this. If I have 2 objects of masses M1 = 50kg and M2 = 80kg and 2 forces - F1 = 1000N and F2 = 5000N, which combination of M and F will produce maximum acceleration, and what would that be?


PS - INTERPRETATIONS OF FORCE AND MASS WRT TO OUR WORLD

I know the concepts of mass and forces seem abstract, so to help you understand better here are some forces and masses that occur in nature. These will help you compare and comprehend these units better.

Selected forces and masses