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

Question

The potential energy stored in the compressedspring of a dart gun, with a spring constant of 66.50 N/m, is 1.040J. Find by how much is the spring is compressed.

A 0.130 kg dart is fired straight up. Find thevertical distance the dart travels from its position when thespring is compressed to its highest position.

The same dart is now fired horizontally from aheight of 2.30 m. The dart remains in contact until the springreaches its equilibrium position. Find the horizontal velocity ofthe dart at that time.

Find the horizontal distance from the equilibriumposition at which the dart hits the ground.

Explanation / Answer

Force constant tk = 66.5. N/ m

Compression x = ?

Energy E = 1.04 J

We know E = ( 1/ 2) kx ^ 2

From this compression x= [ 2E / k]

                                        = 0.1768 m

(b). Mass m = 0.13 kg

Let the vertical distance be h

Then from law of conservation of energy , maximum elasticpotential energy = gravitational potential energy at maximumheight

( 1/ 2) kx ^ 2 = mgh

     1.04 = 0.13 * 9.8 * h

So, R = 2.739 m

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