Physics:roller coaster questions with loops, weight, and angles

[rj101]

Homework Statement

You are on a roller coaster ride, and enter the bottom of a loop of radius r moving at a velocity v0. You decide to measure your initial velocity v0 by using a simple bathroom scale and a little physics. As you go through the loop, the scale you are sitting on reads 5/2 times your weight when you are θ = 30◦ (from the horizontal) above the middle of the loop. If the loop has a radius r = 20/3 m, and gravity has an acceleration of g = 10 m/s2, at what velocity v0 did you enter the loop? What does the scale read (in terms of your weight) at the top of the loop? Be sure to draw and properly label diagrams where appropriate, and assume there is no friction in the problem.

Homework Equations

any equations to do with energy

The Attempt at a Solution

 

[jbsteele]

The initial velocity can be found using the equation for centripetal acceleration:v0 = sqrt(g*r/sinθ)v0 = sqrt(10*20/3/sin30)v0 = 11.06 m/sAt the top of the loop, the scale will read 3/2 times your weight, since the angle θ is 90 degrees from the horizontal.