4 part question. Dart Gun. The potential energy stored in the compressed spring

Question

4 part question. Dart Gun.

The potential energy stored in the compressed spring of a dart gun, with a spring constant of 30.50 N/m, is 1.420 J. Find by how much is the spring is compressed. ______

A 0.110 kg dart is fired straight up. Find the vertical distance the dart travels from its position when the spring is compressed to its highest position. ______

The same dart is now fired horizontally from a height of 2.70 m. The dart remains in contact until the spring reaches its equilibrium position. Find the horizontal velocity of the dart at that time. ______________

Find the horizontal distance from the equilibrium position at which the dart hits the ground. _________

Explanation / Answer

a. F = 30.5x
E=Fd=1.42

1.42=30.5x^2
x=.2158m

b. assume no energy loss

1.42 =mgh
1.42=0.11*9.81*h
h=1.316m

1.42=1/2*m*v^2
v=5.081m/s

y=1/2*g*t^2 (0 vertical velocity)
2.7=1/2*9.81*t^2
t=.7419 seconds to hit the ground
horizontal distance to hit ground=0.7419*5.081m/s
=3.77m

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