# conservation of energy problem?

You are designing a game for small children and want to see if the ball's maximum speed is sufficient to require the use of goggles. In your game, a 18.0 g ball is to be shot from a spring gun whose spring has a force constant of 600 N/m. The spring will be compressed 5.00 cm when in use. How fast will the ball be moving as it leaves the gun and how high will the ball go if the gun is aimed vertically upward?

v0= m/s

hmax= m

also: What would be your recommendation on the use of goggles?

### 2 Answers

- JimLv 74 years agoFavorite Answer
max SPE = 1/2kx² = (0.5)(600)(0.05)² = 0.75 J

0.75 = 1/2mV² = 0.5(0.018)V²

V² = 0.75/(3.24E-3) = 83.333...

V ≈ 9.13 m/s ANS-1

max height of ball = h = V²/2g =83.333.../2(9.81) = 4.25 m ANS-2

- electron1Lv 74 years ago
The work that is done by the spring is equal to the maximum kinetic energy of the ball.

Work = 600 * 0.05 = 30 N * m

KE = ½ * 0.018 * v^2 = 0.009 * v^2

0.009 * v^2 = 30

v = √3333⅓

This is approximately 57.7 m/s. At this velocity, I think the children should wear goggles. As the ball rises to its maximum height, its velocity decreases from this velocity to 0 m/s at the rate of 9.8 m/s each second. Use the following equation.

vf^2 = vi^2 + 2 * a * d, vf = 0, a = -9.8

0 = √3333⅓ + 2 * -9.8 * d

19.6 * d = √3333⅓

d = √3333⅓ ÷ 19.6

This is approximately 2.95 meters

what would be your recommendation of the goggles?