Answer to Question #325718 in Molecular Physics | Thermodynamics for Love

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)

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

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

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