Ablock with mass m 2.00 kg is placed against a spring on a frictionless incline with angle 30 degrees (fig. b-43). (the block is not attached to the spring.) the spring, with spring constant k 19.6 n/cm, is compressed 20 cm and then released. (a) what is the elastic potential energy of the compressed spring? (b) what is the change in the gravitational potential energy of the block - earth system as the block moves from the release point to its highest point on the incline? (c) how far along the incline is the highest point from the release point?

Explanation:

a )

The stored elastic energy of compressed spring

= 1 / 2 k X²

= .5 x 19.6 x (.20)²

= .392 J

b ) The stored potential energy will be converted into gravitational potential energy of the block earth system when the block will ascend along the incline . So change in the gravitational potential energy will be same as stored elastic potential energy of the spring that is .392 J .

c ) Let h be the distance along the incline which the block ascends.

vertical height attained ( H ) =h sin30

= .5 h

elastic potential energy = gravitational energy

.392 = mg H

.392 = 2 x 9.8 x .5 h

h = .04 m

4 cm .

=

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