An acrobat of mass 59.6 kg would like to jump from a substantial height onto a small round trampoline standing on the floor. Although the trampoline is built to act like an ideal spring with spring constant 6.7 x 104 N/m, its taught material cannot withstand an indentation of more than 38.8 cm before tearing. What is the largest height that the acrobat can jump from (as measured from the trampoline top, in metres), so that the trampoline material doesn't tear?

Question

An acrobat of mass 59.6 kg would like to jump from a substantial height onto a small round trampoline standing on the floor. Although the trampoline is built to act like an ideal spring with spring constant 6.7 x 104 N/m,  its taught material cannot withstand an indentation of more than 38.8 cm before tearing. What is the largest height that the acrobat can jump from (as measured from the trampoline top, in metres), so that the trampoline material doesn't tear?

Anonymous · Answer

kinetic energy of acrobat at trampoline = 1/2 m v^2 = m g h = 59.6 * 9.81 * h = 585 h Joules = potential energy in spring when stopped = (1/2) k x^2 = (1/2)(6.7*10^4) (0.388)^2 585 h = 5043 h = 8.6 meters (Yikes !)