Saturday, February 16, 2013

What is Newton's Second Law?

Science for Writers:  Newton's Second Law
'Apple on books' from Science for Writers Logo and text created by me.

Welcome to the latest Science for Writers post. Last time we discussed Newton's First Law. In this, the second of a three part mini-series, I will explain Newton's Second Law of motion.

I have put important words in bold. These words are important in physics and I will refer to them throughout the post. It isn't overly important for you to know the exact meaning, so long as you get the gist of what I'm talking about you will be fine following this post.

Writing Links are in italics and these discuss how the science could be used in writing.

What does it state?

Newton wrote in his book, Principa:
Law II:  The alteration of motion is ever proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed
Lets break it down before going further:

  • Alteration, means change.
  • To motion is movement.
  • Proportional means a change in the first thing causes a change in the second.
  • A motive force is what makes something move
  • The right line means the direction in which the movement is happening
  • Impressed means acting on the object
Now we've split it up, it is easier to understand. In actuality it is just a wordy way of saying, 'the amount an object's motion changes is equal to the force making it change'.

As with all good laws in physics there is an equation to go with it.

However, the actual equation is beyond the scope of this article, but we can derive another equation from it. This is one I am sure you have all heard of:

F = ma

Where the F is force, the m is mass, and the a is acceleration.

I should point out the F=ma is actually a special case where the mass is constant and the object is not moving close the speed of light. In ideal conditions it can be applied to balls rolling and things falling.

F=ma means that if you accelerate an object (that is to change its velocity/speed) you can calculate the force making it accelerate that much. Let's do an example:

An object of 3kg is pushed. It accelerates from stationary to 10 metres per second in 2 seconds. What force is acting to make this change?

First let's calculate the acceleration. Acceleration is the change in velocity over time. So 10 divided by 2 which is 5 metres per second per second (m/s/s).

Well we know that F=ma so we simply need to do F=3x5, which everyone knows is 15. But 15 what? Elephants? Oranges? No. The unit for force is the Newton (N), named after Isaac Newton.

You may be wondering why I chose kilograms and metres per second. These are SI units. An SI unit is one that a central organisation has decided will be the unit for that measurement. The SI unit for mass is the kilogram, for speed is metres per second, for force is the Newton, for distance is the metre, and for time is the second. By using these units the equations will always work. If you start using non-SI units then the equations don't work without further fiddling.

Writing Link:  I mentioned that F=ma is a special case where mass doesn't change. Imagine a rocket. The mass decreases as fuel is used up and less and less force is needed to keep it at a constant acceleration. Now imagine this as a very convoluted analogy for a story. At the start it is 'heavy' and to get it going you need a lot of force. As the story gets going it gets 'lighter'. This means you can either put less force into making the story continue as it is, or you can keep the force and allow the story to gain momentum and increase the pacing.

Another example

Apple Falling
Image from
Creator: Dan Kosmayer
Imagine a 200g (0.2kg) apple being dropped into water. We can calculate the force the water exerts on the apple by measuring it's change in velocity. You can do this with a timer and a ruler (and a good eye). Let's say just before it hits the water it is moving at 2 metres per second. A second after it hits the water it is moving at 0.5 metres per second (m/s). What force did the water exert on the apple?

Well, we need to know the acceleration. It starts off at 2 m/s and 1 second later is 0.5 m/s. So the maths is (0.5-2)/1. / means 'divided by'. This equals -1.5 m/s/s

Now we'll put it into F=ma. F= 0.2kg x -1.5 m/s/s

That means that water exerts a force of 1.3N on the apple and causes it to decelerate.

But what makes the water exert this force on the apple? Well that is to do with Newton's Third Law which we'll look at next week.

Writing Link:  You may have been able to tell that Newton's Second Law doesn't lend itself to writing that nicely. It is essentially maths so aside from doing maths in your book there's not much to say. However, you could have a maths-y or science-y character that refers to the laws in conversation. Perhaps the other characters don't like this, perhaps they enjoy the lessons. You decide.

So, there you have it, Newton's Second Law. Please comment on this post below; I'd love to here from you. Share this post if you enjoyed it. There are social media buttons at the bottom of the post for your convenience.



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