Case Studies - Circular Motion - Questions 11 Help

Velocity is a vector that is fully described by a numerical value (such as 20 m/s) and a direction. Objects that move along a circular path have a velocity vector that is directed tangent to the path. Such objects are also experiencing an acceleration and a net force. Acceleration and net force are both vector quantities that have a direction that is towards the center of the circle.

What This Question Isn't About

Physics is a course that can be filled with formulas. And one way that students often use those formulas is as a recipe to solve problems. They are given numerical values for some of the variables in the equation. They plug those values into the equation. Maybe they do some algebraic manipulation of the equation. And finally they solve for the unknown value. That's not what's going on in this question. Put your calculator and your plug-and-chug mentality away because they won't do you much good on this question.

 

What This Question Is About

In this question, you will need to use the F = m•v²/R equation. But you need to use it as a guide to thinking about how differing m, v and R values would affect the net force experienced by an object. In this question, you will have to think proportionally. That's quite different than plug-and-chug thinking.

 

Here's How to Think About It:

So thinking about the F = m•v²/R equation involves proportional reasoning. The net force is directly proportional to the square of speed AND inversely proportional to the radius. If one case has two times the speed then it would have four times the net force. And if one case had one-half the speed, then it would have one-fourth the net force. You will need to find the multiplying factor that results from any difference in speed value between the two cases.

But that's not all. You also have to consider the radius. And the thinking works differently for radius since the net force is inversely proportional to the radius. If Case A has one-half the radius, then that would result in two times the net force. And if Case A has two times the radius, then that would result in one-half the net force. You will need to find the multiplying factor that results from any difference in radius value between the two cases.

Now once you have determined the multiplying factor for speed and the multiplying factor for the radius, you can put the two multiplying factors together to determine the answer. You will have to multiply the multipying factors. Take your time ... maybe jot down a note on some scratch paper ... and work out the answer thoughtfully using the proportional reasoning described in the previous two paragraphs.