Question

A vertical spring (ignore its mass), whose spring constant is 825 N/m , is attached to a table and is compressed down by 0.160 m.

A)What upward speed can it give to a 0.360-kg ball when released? Express your answer to three significant figures and include the appropriate units.

B) How high above its original position (spring compressed) will the ball fly? Express your answer to three significant figures and include the appropriate units.

Answer 1

Given

vertical spring with spring constant k = 825 N/m

compressed to a distance of x = 0.160 m

A) mass on the spring(ball) is m = 0.360 m

As long as the mass is on the spring with some external force making the spring to compress the elastic potential energy will be developed in the spring

the moment, force removed on the mass , then the elastic potential energy will be converted in to kinetic energy of the mass

first the elastic potnetial energy of the spring is,E.P.E = 0.5*k*x^2

   E.P.E = 0.5*825*0.160^2 J = 10.56 J
this energy will be imparted to the mass and move upward with initial kinetic energy k.e

   k.e = 0.5*m*v^2 = 0.5*0.360*v^2 = 10.56 J

solving for 'v', v = 7.769 m/s

B) the height of the ball can reach is , the kinetic energy of the ball will be converted in to gravitational potential energy

   k.e = G.P.E

   k.e = m*g*h

   h = k.e/m*g

   h = 10.56/(0.360*9.8) m

   h = 2.993 m
the Height reached by the ball from the point of spring compression is h = 2.993 m