A 36 g ball is shot from a spring gun whose spring has a force constant of 529 N

Question

A 36 g ball is shot from a spring gun whose spring has a force constant of
529 N/m. The spring can be compressed 4 cm. How high will the ball
go if the gun is aimed vertically? The acceleration of gravity is 9.81 m/s2.
Assume that at the end of the barrel, the spring A 36 g ball is shot from a spring gun whose spring has a force constant of
529 N/m. The spring can be compressed 4 cm. How high will the ball
go if the gun is aimed vertically? The acceleration of gravity is 9.81 m/s2.
Assume that at the end of the barrel, the spring

Explanation / Answer

The potential energy of the spring is (1/2)k*x^2. This energy gets imparted into kinetic energy of the ball which is then converted to gravitational potential energy (ignoring any frictions, etc)).

(1/2)k*x^2 = m*g*h

h = (1/2)[k/(m*g)]x^2

h = (1/2)[529/(0.036*9.81)](0.04)^2

h = 1.198 meters

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