Jessie (m=56.2 kg) is traveling at a speed of 12.8 m/s at the top of a 19.5-m high roller coaster loop.

Question

Jessie (m=56.2 kg) is traveling at a speed of 12.8 m/s at the top of a 19.5-m high roller coaster
loop. 

What force does Jessie feel from her seat at the bottom of the loop? (ans: 3707N)

We found speed at the bottom of the loop=23.4m/s

I am using the formula Fc=(v^2/r) x m

V=23.4m/s  r=19.5/2=9.75m and m =56.2kg 

I keep getting 3156N not 3707N 

Answer 1

u = speed at top = 12.8 m/s

h = initial height = 19.5 m

v = speed at bottom = ?

 

Use energy conservation to get v.

 

mv²/2 + mg(0) = mu²/2 + mgh

 

v²/2 = u²/2 + gh

 

v = √(u² + 2gh) = √[12.8² + 2(9.8)(19.5)] m/s ≅ 23.4 m/s   [We agree so far.]

 

F_n = upward force at bottom

 

The radius is h/2.  At the bottom,

 

F_n - mg = mv²/(h/2) = 2mv²/h

 

F_n = 2mv²/h + mg = m(2v²/h + g) = (56.2)[2(23.4)²/19.5 + 9.8] N ≅ 3707 N