# What work does a force of 8 N do when the spring is stretched 6 cm?

December 29, 2020 | education

| F = 8 N.

x = 6 cm = 0.06 m.

A -?

The work A performed during the stretching or compression of the spring, according to the law of conservation of energy, is equal to the change in its potential energy ΔEp: A = ΔEp.

Since initially the spring was in an unstretched state Еп0, then ΔЕп = Еп – Еп0 = Еп.

The potential energy of the spring Ep is determined by the formula: En = k * x2 / 2, where k is the stiffness of the spring, x is the change in the length of the spring.

The spring stiffness k is found from Hooke’s law: F = k * x.

k = F / x.

A = F * x2 / 2 * x = F * x / 2.

A = 8 N * 0.06 m / 2 = 0.24 J.

Answer: when the spring was stretched, mechanical work A = 0.24 J.

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