Car & Roller Coaster Centripetal Force Problems

How To Do Car, Plane & Roller Coaster Centripetal Force Problems

All these problems have certain things in common, so this first video takes you through the basics and explains how to see through the blah blah blah of your typical physics problem to recognize the problem underneath.

Centripetal Force Problem - Car Doesn't Lose Contact With Ground

This classic centripetal force problem describes a small hill in a road as "approximately circular", and then asks the maximum speed that a car can go over that hump without "loosing contact with the road", or some other description that translates to "set the normal force equal to zero." Basically: don't do a Dukes of Hazzard over that speed bump!

Maximum G-Force At Bottom of Plane Loop-to-Loop

When a military jet does a vertical loop, the pilot is "pulling g's", getting squished down into her seat. In this problem (or similar ones involving roller coasters), they ask you to calculate the minimum radius such that the pilot doesn't pull more than a certain number of g's that would make her pass out.

Jet Speed At Top of Loop To Experience Weightlessness

This problem is just like the previous one about a car going over a hump in the road: calculate the speed such that the pilot feels weightless. Once again you're setting normal force equal to zero, except this time it's normal force of air on the wings (or the seat on the pilot's butt) rather than the force of the tires on the road.

Roller Coaster Speed at Top of Loop To Maintain Contact With Track

Once again we're setting normal force equal to zero, except this time it's to find the speed at which a roller coaster car "loses contact with the track" or "passengers don't leave their seats".

Centripetal Force - Minimum Coefficient of Friction To Prevent Car Skidding

In the first of a few problems about cars going around turns, in this case the road is level - not banked - and we'll calculate the minimum coefficient of static friction to prevent the car from skidding.

Centripetal Force - Bank Angle For Road To Prevent Car Sliding (no friction)

This is another classic car problem, in which they tell you that the road is so slippery that there is no friction at all, and then they ask you to calculate the angle that the road should be banked to keep the car going nicely through the turn without sliding to the outside or inside of the turn.

Centripetal Force - Max Speed of Car Around Banked Curve (with friction)

The hardest of these banked turn problems. The bummer is that both friction and normal force are at angles because of the bank, so you have to break them both up into X & Y components. It's not impossible, but it does make for some juicy algebra and trig as you attempt to solve a system of two equations and two unknowns, one of which is stuck inside trig functions!

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