# Centripetal physics homework

So i’ve got this problem i think you guys can help me with

A roller coaster is at the bottom of a loop 30 meters in diameter.
at the bottom of the loop, the person in the car feels 1.5 times heavier than their true weight.
What is the roller coaster’s speed at the bottom of the loop?

This question’s got me stumped. some help from you guys would really help me out.

If they were sitting in a chair next to the roller coaster, the only accelleration they’d feel would be gravity, which is 9.8 m/sec/sec. Any excess acceleration comes from the change in velocity from moving on a 30 m circular loop. (I’m assuming circular loop, or 30 m is the radius of curvature at the bottom of the loop – same thing.)

Is that enough to get you going?

here’s what i have so far. but it’s not too concvincing.

The force exerted due to the loop is 1.5 times that of gravity, right? which means that the acceleration along the loop is 14.7 m/s squared as opposed to the 9.8 it would usually be.
the formula for centripetal force is F = - ( mv^2 / r ) r
so 14.7=-(9.8v^2/30)30 right?

but then the answer i got for velocity was 1.22 meters per second.

not convincing. where am i going wrong?

No, weight means force. Like Fn, not acceleration.

I got: EF = ma = Fn-mg = mv^2/r
(EF) is %sigma F

It gave me a realistic answer.

in this equation, what value do you input for m? i know normal force would be 14.7, and the g would of course be 9.8 what are the other factors?

When considering just one unit of mass, weight is equal to acceleration. F=ma, if m==1, F=a

alright guys, thanks. you really helped otu here. i was pretty much lost as to where to go, but im prety sure i got the answer right.

by the way, i think the answer was 12.12 meters per second.

we’ll see if i gotit right!

What you need to do, is set up the equation like EF = ma = ____ and then solve for your desired variable before plugging in numbers. Many times, mass or other unknonwns will cancel themselves out (mass did in the last problem).

That answer is roughly what I got (I can’t remember, except that it was 12.??)

F=(mv^2)/r
(unit mass, so m=1)
v=sqrt(F*r)
since r=15
v=sqrt(15 F)

Hmm, if by 1.5 times heavier, they mean 1.5 times extra force (so a total force of 2.5g), then
v=sqrt(15*14.7)
v=14.85

Otherwise it means the total force felt was 1.5g, then the loop only contributes 0.5g.
v=sqrt(15*4.9)
v=8.57 m/s

12.12m/s is the speed you’d need to simulate gravity in a 0-g environment with a 15m radius loop.

the formula for centripetal force is F = - ( mv^2 / r ) r

The second r should have a hat over it, it means the unit vector, which is there because it’s for calculating a vector. Basically just means “in the direction of r”.

Edit- Really shouldn’t use more than one decimal place here, since that’s what you’ve got going in.