The potential energy stored in the compressed spring of a dart gun, with a sprin

Question

The potential energy stored in the compressed spring of a dart gun, with a spring constant of 48.50 N/m, is 1020. Find by how much is the spring is compressed Submit Answer Tries 0/5 A 0.030 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. Submit Anawor Tries 0/5 The same dart is now fired horizontally horizontal velocity of the dart at that time ori zontai delocit or thedareznalrfteom a height of 1.50 m. The dart remains in contact until the spring reahess equilibrium position. Find the Submit Answer Tries 0/5 Find the horizontal distance from the equilibrium position at which the dart hits the ground

Explanation / Answer

k = spring constant = 48.5 N/m

U = potential energy stored in the spring = 1.020 J

x = compression of the spring = ?

Using the formula

U = (0.5) k x2

1.020 = (0.5) (48.5) x2

x = 0.21 m

h = height gained from the compressed position

m = mass of the dart = 0.03 kg

using conservation of energy

Potential energy gained = spring potential energy

mgh = U

(0.03) (9.8) h = 1.020

h = 3.5 m

v = horizontal velocity

Using conservation of energy

kinetic energy gained = spring potential energy

(0.5) m v2 = U

(0.5) (0.03) v2 = 1.020

v = 8.25 m/s

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