Answer to Question #329397 in Mechanics | Relativity for Jane

Question

An ideal spring of negligible mass with force constant of 400 N/m is placed on a frictionless horizonal

table with one end fixed at a wall next to the table. A billiard ball of mass 200 g is pushed against the spring, compressing the spring to some distance. After the system is released, the spring returns to equilibrium with the billiard ball leaving the table's edge at 4.00 m/s and hits the floor 80 cm below. Using the principle of energy conservation, (a) determine the initial compression of the spring. (b) What is the speed of the ball when it hits the floor?

Answer 1

a)

$\frac{kx^2}2=\frac{mv^2}2,$

$x=v\sqrt\frac mk=9~cm,$

b)

$\frac{mu^2}2=mgh,$

$u=\sqrt{2gh}=4~\frac ms,$

$v'=\sqrt{v^2+u^2}=5.7~\frac ms .$