A ball with a mass of #420 g# is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of #21 (kg)/s^2# and was compressed by #6/5 m# when the ball was released. How high will the ball go?

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Answer 1 · 2017-10-15T02:02:48

7.34 m

Potential energy in spring when it’s in compressed state is
#U = (kx^2)/2#

#U = (21 kgs^-2 × (6/5 m)^2) / 2 = 15.12 J#

According to law of Conservation of Energy
Total energy stored in spring = Total energy gained by ball

#15.12 J = (mgh)/2#

#h = (2 × 15.12 J) / (mg)#

#h = (2 × 15.12 J) / (420 text(grams) × 10^-3 text(kg/grams) × 9.8 ms^-2)#

#h = 7.34 m#