A jet makes two loops in vertical circles. The highest point of both circles is 3200 m above the ground.?

Question

The 65.0 kg pilot sits on a scale. Take g = 10.0 m/s2.

1.On the first loop, the jet comes within 665 m of the ground. The pilot notices that her scale reading at the top of the loop is 325 N. How long does it take to complete this loop?

I know that radius is approx. 1276, but I do not know how to find acceleration when the pilot is right-side up and up-side down.


Thanks in advance!

Answer 1

I assume the jet moves with constant speed ?

When at the top of the loop there will be gravity pulling straight down
650 N

and centripetal force radial to the center of the loop pushing her upward into the seat
=m*v^2/r
where v is the tangential speed and r is the radius
therefore

325=2*65*v^2/(3200-665)-650

solve for v
v=138 m/s

To circumnavigate the entire circumference of the loop
2*pi*(3200-665)/v
or
115 seconds

j