Question

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.

Answer 1

Answer:

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