Question

4. A marble of mass m initially at rest at height h moves along a frictionless rail that forms a hoop of radius R. At the end of the rail the marble hits a spring of elastic constant K. Calculate: (a) the minimum value of h for which the marble hits the spring (b) the maximum compression of the spring for that value of h 5mqR nswer (a in2

Answer 1

(a) Marble enters into the hoop and makes one complete loop to loop motion and the exits from the loop and strikes with the spring. For complete loop to loop motion rightarrow the minimum velocity as marble at the lowest position as hoop = squareroot 5gR So squareroot 2gh = squareroot 5gR h_minimum = 5R/2 h minimum = 5/2 R (b) From conservation as energy rightarrow mgh = 1/2 k(Delta_x)^2 Delta_x = squareroot 2mgh/k = squareroot 2mg times 5/2 R/k or Delta_x = squareroot 5 mgR/k Delta_x = squareroot 5 mgR/k