Question

if 30.0 J of work are required to stretch a spring from a 4.00 cm elongation to a 5.00cm elongation, how much is needed to stretch it from a 5.00cm to a 6.00cm elongation

Answer 1

The energy required to stretch the spring from a 5.00cm to a 6.00cm elongation is 30 J

From Hooke's law, Force = Elastic constant * extension

F = K*e

K = Elastic constant; e = extension

• Work done = K*e²/2

• Work done = 30.0 J

• e = 5.00 - 4.00 m

• e = 1.00 cm or 0.01 m

solving for K

• K = 2 * work done/e²

• K = 2 * 30.0 / (0.01)²

• K = 600000 N/m

The energy required to stretch the spring from 5.00 to 6.00 cm is then calculated;

• e = 6.00 cm - 5.00 cm

• e = 1.00 cm = 0.02 m

• W = 600000 * (0.01)² / 2

• W = 30 J

Therefore, the energy required to stretch the spring from a 5.00cm to a 6.00cm elongation is 30 J

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