A single-car loop-the-loop is launched by means of a giant spring (k = 30 kN/m).
ID: 2134513 • Letter: A
Question
A single-car loop-the-loop is launched by means of a giant spring (k = 30 kN/m). The car (m=900kg) is placed at rest againts the spring which has been compressed by a distance, d. When released, the spring propels the car into a frictionless vertical circular track of radius R = 7.0m.
a)Using numerical methods of Chapter 8, find an algebraic expression (That is without any numerical values for the quantities) for the smalled that d can be if the car is to stay on the track
b) Find numerical value for d.
Explanation / Answer
KE of car = 0.5*30*d^2 = 15d^2 = 0.5*900*v^2 = 450v^2
d^2 = 30v^2
mg = mv^2/R = mv^2/7 = md^2/210
d^2 = 210g = 210*9.8
d = 45.36m