Super Fun Rollercoaster Problem

Homework Statement

A roller coaster car is going over the top of a 14-m-radius circular rise. At the top of the hill, the passengers "feel light," with an apparent weight only 60 % of their true weight. How fast is the rollar coaster going?

My problem first is I am unsure where the normal force is going - my professor said that with centrifical motion the normal force is always inwards, but I remember when we did this problem he made it upwards. Then, he set mg - N = mv²/r. I just don't understand how he got the left side, why is it mg - N and not the other way around? Does it matter?

Homework Equations

a=v²/r

The Attempt at a Solution

N=1.5mg

N - mg = mv²/r

0.5(mg) * r = v²

 

[kuruman]

To begin with, the normal force is always away from the surface. A surface cannot pull on an object, it can only push on it. At the top of the track there are two possibilities
(a) If the roller coaster is on the outside, the normal force is up opposite to gravity.
(b) If the roller coaster is on the inside, the normal force is down, in the same direction as gravity.

In the example that your professor showed you it seems that the roller coaster was on the outside. It also seems that he assumed that "down" is positive. In that case the normal force is "up" (negative) and the weight (down) is positive. Thus, the net force is mg - N. The right side is positive (down towards the center) and equal to mv²/r. So mg - N = mv²/r.

 

To begin with, the normal force is always away from the surface. A surface cannot pull on an object, it can only push on it. At the top of the track there are two possibilities
(a) If the roller coaster is on the outside, the normal force is up opposite to gravity.
(b) If the roller coaster is on the inside, the normal force is down, in the same direction as gravity.

In the example that your professor showed you it seems that the roller coaster was on the outside. It also seems that he assumed that "down" is positive. In that case the normal force is "up" (negative) and the weight (down) is positive. Thus, the net force is mg - N. The right side is positive (down towards the center) and equal to mv²/r. So mg - N = mv²/r.

Okay, what you said about the N makes a lot of sense, thanks! As for the question, you're saying that the ma is positive as well, but why?

 

[kuruman]

Because in this example "down" has been chosen as positive. When the roller coaster is at the top of the track, its acceleration is towards the center which is "down", therefore positive. When the roller coaster is at the bottom of the track, its acceleration is still towards the center which in this case is "up" therefore negative.