In a spring gun, a spring of mass 0.240 kg and force constant 3100 N/m is compressed 2.00 cm from its unstretched length. When the trigger is pulled, the spring pushes horizontally on a 5.5*10-2 kg ball. The work done by friction is negligible. Calculate the ball's speed when the spring reaches its uncompressed length ignoring the mass of the spring.

The ball's speed when it reaches its uncompressed length = 0.73m/s

Explanation:

The speed of the ball is greatest when acceleration is zero and the net force on the ball is zero.

Given:

Force constant = 3100Nm

Compressed length = 2.0cm = 0.02m

Spring mass = 0.240kg

Mass of barrel = 5.5 * 10^-2kg

Resistant force, F = ma

F = 5.5*10^-2 * 9.8 = 0.539N

0.538/3100 = 1.738*10^-4m

Initial force on the ball = (3100 * 0.02) - 0.539

Initial force on ball = 62 - 0.539 = 61.46N

Final net force on ball = 0N

Mean net force of ball = 1/2 (61.46 + 0) = 30.73N

Net on ball = 30.73 * (1.74*10^-4) = 5.35*10^-3J

Transfer to KE = 1/2mv^2

V^2 = (5.35*10^-3) / 0.01

V^2=0.535

V = Sqrt (0.535)

Vmax = 0.73m/s