Course Contents....Set 04 (10/10 Tu 11:59 PM) Dart gun The potential energy stor

Question

Course Contents....Set 04 (10/10 Tu 11:59 PM) Dart gun The potential energy stored in the compressed spring of a dart gun, with a spring constant of 56.50 N/m, IS spring is compressed. Sebmit Answer Tries 0/12 osition Submit Answer Tries 0/12 A 0.090 kg dart is fired straight up. Find the vertical distance the dart travels from its position when the spring is compressed to i horizontal velocity of the crart at that tima, height of 3.10 m. The dart remains in contact until the spring reaches its equilibrium position. Find Suemit Answer Tries 0/12 Find the horizontal distance from the equllibrium position at which the dart hits the ground. Tries 0/12 Send Feedback Post Discussion

Explanation / Answer

Given,

k = 56.5 N/m ; U = 0.8 J

We know that the stored energy of the spring is given by:

U = 1/2 k x^2

x = sqrt (2 U/k)

x = sqrt (2 x 0.8/56.5) = 0.1682 m

Hence, x = 0.1682 m = 16.82 cm

from conservation of energy:

m g h = U = 0.8 J

h = 0.8/mg = 0.8/0.09 x 9.81 = 0.91 m

Hence, h = 0.91 m

from conservation of energy:

1/2 m v^2 = 0.8

v = sqrt ( 2 x 0.8/0.09) = 4.22 m/s

Hence, v = 4.22 m/s

time to reach ground

t = sqrt(2h/g) = sqrt(2 x 3.1/9.81) = 0.79 s

D = vt = 4.22 x 0.79 = 3.33 m

Hence, D = 3.33 m

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