A dart of mass m = 5.50 g (0.0055 kg) is loaded into a toy dart gun and the gun

Question

A dart of mass m = 5.50 g (0.0055 kg) is loaded into a toy dart gun and the gun is held horizontally. The spring in the gun has a spring constant of k = 150 N/m. The spring in the gun is compressed a distance 4.5 cm (0.045 m) when the gun is cocked. When the trigger is squeezed, the spring decompresses and the dart is released when the spring reaches its natural length at the muzzle of the gun. The dart then shoots out of the gun and strikes the bulls eye of a target. Ignore friction and air resistance.

Explanation / Answer

Energy stored in the spring = 0.5*k*x^2 = 0.5*150*(0.045^2) = 0.15 J

Potential Energy loss = m*g*(Change in height) = 0.0055*9.8*(0.9-0.5) = 0.02 J

This energy is converted to inetic energy

So according to the conservation of energy

0.15 + 0.02 = 0.5*m*v^2

v^2 = 0.17/(0.5*0.0055) = 61.81

v = 7.86 m/s

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