Question

A mass of 9 kg is placed on a horizontal frictionless surface and attached to a spring. The mass is compressed 0.69 meters on the spring from equilibrium and held still. It is then released and it travels across the horizontal surface, around a frictionless quarter circular ramp, and it is launched into the air vertically and reaches a maximum height of 6 meters above the ground. The same mass is then attached to the same spring and hung vertically from a ceiling. How far does the spring stretch before the acceleration is zero, in centimeters

Answer 1

energy remain conserve

apply from spring PE to maximum height

at maximum height here is no velocity so there is only PE

1/2 * kx^2 = mgh

k = 2mgh/x^2

k = 2 * 9 * 9.8 * 6 / 0.69^2

k = 2223.06 N/m

now acceleration = 0 means all forces sum is zero

Fspring = Fgravity

kx = mg

x = mg/k

x = 3.9675 cm