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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