If the spring of a jack in the box is compressed a distance of 8.00 cm from its relax

The potential energy stored in the compressed spring is converted to the gravitational potential energy of the toy when it moves in the vertical direction upon release, and the kinetic energy of the toy. The potential energy of the compressed spring is (1/2)(k)(x)^2 = (1/2)(80 N/m)(0.08 m)^2 = 0.256 J. The gravitational potential energy of the toy when it is at the spring's relaxed length is mgh = (0.05 kg) x (9.81) x (0.08m) = 0.04 J. Hence the kinetic energy of toy at relaxed length is (3.2 - 0.04) J = (0.256 - 0.04) J = 0.216 J. Hence the velocity of the toy head is 0.216 J = (0.5)(0.05 kg)(v^2), v = sqrt(0.216J/0.025 kg) = 2.94 m/s.

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