What Is the Correct Formula for Calculating Speed in Uniform Circular Motion?

[d.tran103]

Can someone tell me how I am plugging this in wrong? And am I using the right equations? Thanks!

Homework Statement

A pilot is flying a vertical loop of radius 290 m, and at the top of the loop is pushing against the seat with a force of .25 "g's" {or Normal force = .25mg}. What is the speed of the airplane at that moment?

In the above loop problem, if at the bottom of the loop the pilot is pushing against the seat with 6.0 "g's", what is his tangential or linear speed?

Homework Equations

v^2/r = a-g

The Attempt at a Solution

I plugged everything in but keep getting a negative number that cannot be square rooted. This is what I'm plugging in. How am I plugging this in wrong?

v^2/290 = 9.8*(0.25) - 9.8

 

[d.tran103]

My choices for part a are:
60 m/s
77 m/s
53 m/s
81 m/s

This makes no sense!

 

[Mr.A.Gibson]

At the top of the loop the forces acting on the pilot are the seat pushing on him and gravity. Hence the total force is

F = mg + 0.25mg
= 1.25mg
also
$$F = ma = mv^2/r$$

equate these two and resolve for v

At the bottom of the loop, again calculate the resultant force and use the same method to solve.

 

[ashishsinghal]

Here use v^2/r = a+g.
Because a, v^2/r and g have the same direction

 

[ashishsinghal]

v^2/r = a-g

Here use v^2/r = a+g.
Because a, v^2/r and g have the same direction