A ball with a mass of #500 g# is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of #16 (kg)/s^2# and was compressed by #8/3 m# when the ball was released. How high will the ball go?

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Answer 1 · 2016-06-03T13:43:01

#h=11.6" "meters#

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#"The potential energy that is stored at any spring can be calculated using formula:":#
#E_p=1/2*K*Delta x^2#

#E_p:"Potential Energy"#

#"K:Spring Constant"#

#Delta x:"amount of compress or stretch"#

#E_p=1/2*16*(8/3)^2#

#E_p=8*64/9=512/9" "J#

#"while object is rising ,"E_p" turns to the gravitational potential energy "#

#512/9=m*g*h#

#m=500 " "gr=0.5" "kg#

#g=9.81 " "N/(kg)#

#512/9=0.5*9.81*h#

#h=512/(9*0.5*9.81)#

#h=11.6" "meters#