A ball with a mass of #480 g# is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of #24 (kg)/s^2# and was compressed by #8/9 m# when the ball was released. How high will the ball go?

1 Answer
Sep 29, 2017

Answer:

6.28 m/s

Explanation:

If Spring compressed by #x# then Potential Energy stored in it
#U=1/2kx^2#
#k="spring constant" =24 (kg)/s^2#
#x="Displacement "=8/9 m#

#U=1/2(24)(8/9)^2=(24xx64)/(2xx81)=9.48 J#

After Release spring loaded contraption Potential Energy Changes into Kinetic Energy. (Conservation of Energy)
Hence Mass of 480g has Kinetic Energy #1/2mv^2#

Now Using Conservation of Energy
#"Kinetic Energy"="Potential Energy"#
#U=1/2mv^2#
#9.48=1/2(0.48)(v)^2#
#v^2=39.50#
#v=sqrt39.50#
#v=6.28 m/s#