A 1.00 kg block slides with a speed of 0.920 m/s on a frictionless horizontal su

Question

A 1.00 kg block slides with a speed of 0.920 m/s on a frictionless horizontal surface until it encounters a spring with a force constant of 491 N/m . The block comes to rest after compressing the spring 4.15 cm.

a.) Find the spring potential energy, U, the kinetic energy of the block, K, and the total mechanical energy of the system, E, for compressions of 0 cm.

b.) Find the spring potential energy, U, the kinetic energy of the block, K, and the total mechanical energy of the system, E, for compressions of 1.00 cm.

c.) Find the spring potential energy, U, the kinetic energy of the block, K, and the total mechanical energy of the system, E, for compressions of 2.00 cm.

d.) Find the spring potential energy, U, the kinetic energy of the block, K, and the total mechanical energy of the system, E, for compressions of 3.00 cm.

e.) Find the spring potential energy, U, the kinetic energy of the block, K, and the total mechanical energy of the system, E, for compressions of 4.00 cm.

Explanation / Answer

U = 0.5kx2 and K = 0.5mv2

*Note, by law of conservation of energy, E will remain same in all cases

a) U = 0 ... as spring is uncompressed

K = 0.5 x 1 x 0.922 = 0.4232J

E = U + K = 0.4232J

b) E = 0.4232

U = 0.5 x 491 x 0.012 = 0.02455J

K = E - U = 0.39865 J

c) E = 0.4232

U = 0.5 x 491 x 0.022 = 0.0982J

K = E - U = 0.325 J

d) E = 0.4232

U = 0.5 x 491 x 0.032 = 0.22095J

K = E - U = 0.20225 J

e) E = 0.4232

U = 0.5 x 491 x 0.042 = 0.3928J

K = E - U = 0.0304 J

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