### Video: Newton's Second Law

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Full Length Video Tutorial: Newton's Second Law

#### Newton's Second Law and Proportional Reasoning

Video Transcript

Introduction
What does Newton's Second Law say? And how can one use Newton's Second Law to predict the effect that changes in net force or mass have upon acceleration? I'm Mr. H and I have some answers for you.

Newton's Second Law
One of the assertions of Newton's second law is that the acceleration of an object depends on the net force (Fnet) experienced by the object and the mass (m) of the object. In fact, the acceleration is directly proportional to the net force and inversely proportional to the mass.  This is often expressed by the equation a = Fnet/m.

Acceleration and Net Force
Let's begin with the acceleration-net force relationship. The net force, or Fnet, is the combined effect of all the force vectors. Acceleration is directly proportional to Fnet. That means whatever change is made to Fnet, the acceleration is changed by the same factor. If Fnet is doubled, then acceleration is doubled. If Fnet is tripled, then acceleration is tripled. If Fnet is halved, then acceleration is halved. And so forth. Let's try some practice problems.

Here's a typical problem. We're given an acceleration - 24 m/s/s - and told that there's a change in the Fnet value. We must calculate the new acceleration. We will use this table to as an organizer. The strategy involves determining the multiplying or dividing factor needed to change the 24 m/s/s to a new acceleration value.

In Row #1, the Fnet is doubled ... multiplied by 2. So the same change must be made to acceleration. The multiplying factor for acceleration is 2. The new acceleration is 24 m/s/s multiplied by 2 - that is, 48 m/s/s. In Row #2, the Fnet is tripled ... or 3X larger. So the new acceleration must be 3X larger ... 72 m/s/s. In Rows #3 and #4, the Fnet is decreased. So the acceleration also decreases. We need a dividing factor in order to make the 24 m/s/s smaller. In Row #3, the Fnet is halved ... think of that as divided by 2. So the new acceleration is the 24 m/s/s ÷ 2 = 12 m/s/s. And finally in Row #4, the Fnet is one-fourth the original value; i.e., divided by 4. So the new acceleration value is 24 m/s/s ÷ 4 = 6 m/s/s.

Notice in each row: whatever change was made to the Fnet, the same change was made to the acceleration.

Acceleration and Mass
Acceleration and mass (m) are inversely proportional. That means that whatever change is made to the m, the acceleration is changed by the "inverse" or reciprocal factor. If m is doubled, then acceleration is halved. If m is tripled, then acceleration is one-third the original value. If m is halved, then acceleration is double the original value. And so forth. Let's practice.

In these problems, the mass is being changed. We have to find the resulting acceleration. Once more, we need to find a multiplying or dividing factor. We will use the table to organize our solutions.

In Row #1, the m is doubled ... multiplied by 2. Since m becomes larger, a should become smaller. We need a dividing factor. The new acceleration is the original value divided by 2. In Row #2, the m is tripled. So the new acceleration is 24 m/s/s divided by 3. In Row #3, the m is made smaller so the acceleration must increase. We will need a multiplying factor. Since the m is ½ the size, the acceleration must be two times larger - 48 m/s/s. And in Row #4, the m is 4 times smaller (1/4 the size) so the resulting acceleration will be 4X larger - 96 m/s/s.

Notice in each row: whatever change was made to the m, the inverse change was made to the acceleration.

Multiple Changes
In situations where both Fnet and m are changed, you must make two changes to the acceleration. Be systematic. Apply the same principles. Take your time. Organize your work. Here's a practice problem:

An object has an acceleration of 24 m/s/s. If the net force were tripled and the mass were doubled, then its new acceleration would be _____ m/s/s.

The two changes are: three times the Fnet and two times the m. When Fnet increases, the acceleration increases. You need a multiplying factor of 3. And when m increases, the acceleration decreases. You need a dividing factor of 2. The new acceleration is calculated as ...

24 m/s/s x 3 ÷ 2 = 36 m/s/s.

Conclusion
Mastering a Physics concept requires practice. And we have some awesome interactive exercises on our website that allow you to check to see if you got this.  You can find links to them in the Description section of this video. Give one of them a try. Hey I'm Mr. H. Thanks for watching!

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