A ball with a mass of #640 g# is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of #32 (kg)/s^2# and was compressed by #7/8 m# when the ball was released. How high will the ball go?

1 Answer
Douglas K.
May 6, 2017

#"height" = 1.95"m"#

Explanation:

Begin by converting the mass of the ball to kilograms:

#m = 640"g" rarr 0.64"kg"#

The reference, potential energy of the spring , gives us the equation:

#U_"el"= 1/2kx^2" [1]"#

we are given: #k = 32"kg"/"s"^2# and #x = 7/8"m"#

Assuming that all of the potential energy in the spring is transferred to the ball, the maximum height can be computed, using the equation for potential energy due to height:

#P.E. = mgh" [2]"#

Set the right side of equation [1] equal to the right side of equation [2]:

#mgh= 1/2kx^2#

where #m = 0.64"kg"# and #g=9.8"m"/"s"^2#

#h = ((32"kg"/"s"^2)(7/8"m")^2)/(2(0.64"kg")(9.8"m"/"s"^2)"#

#h = 1.95"m"#

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