A 700 g block is released from rest at heighth0 above a vertical spring with spr

Question

A 700 g block is released from rest at heighth0 above a vertical spring with spring constantk = 450 N/m and negligible mass.The block sticks to the spring and momentarily stops aftercompressing the spring 18.0 cm. (a) How much work is done by the block on thespring? (b) How much work is done by the spring on the block? (c) What is the value of h0? (d) If the block were released from height2.00h0 above the spring, what would be themaximum compression of the spring? Work done by the spring is the negative ofthe change in the spring's potential energy. (c)Did you conservethe mechanical energy? Initially: Is there elastic potentialenergy? Kinetic energy? Gravitational potential energy? If thelatter, you need to define a reference level (y = 0) wheremgy is 0. At the momentary stopping point, what are theelastic potential energy, the kinetic energy, and the gravitationalpotential energy?

Explanation / Answer

Spring constant k = 450 N / m

Initial height h = 2 ho = 2 * 0.8827 m = 1.7654 m

Change in potential energy = eleastic potential energy of thespring

                      Mg( h+ X ) = ( 1/ 2) k X ^ 2

                0.7 kg * 9.8 m / s ^ 2 * ( 1.7654 + X ) = 225 X^ 2

            6.86 X + 12.11 = 225 X ^ 2

225 X ^ 2 -6.86 X -12.11 = 0

                                

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