Question #13046

30 j of work is used to stretch a spring from 2 cm to 4 cm. how much will it take to stretch it from 4 cm to 6 cm? use the equation u=-1/2kx^2

Expert's answer

Let's find coefficient k. We know that 30 j of work is used to stretch a spring from 2 cm to 4 cm, so

30 = U(4) - U(2) = -0.5k4² - 0.5k2² = -10k ==> k = -30/10 =& -3 J/cm².

Thus, the work needed to stretch it from 4 cm to 6 cm is

U = U(6) - U(4) = -0.5k6² - 0.5k4² = -0.5*(-3)*(6² - 4²) = 30.

We see that the work used to stretch a spring from 2 cm to 4 cm is equal to work needed to spring from 4 cm to 6 cm, cause the extension is the same in both cases.

30 = U(4) - U(2) = -0.5k4² - 0.5k2² = -10k ==> k = -30/10 =& -3 J/cm².

Thus, the work needed to stretch it from 4 cm to 6 cm is

U = U(6) - U(4) = -0.5k6² - 0.5k4² = -0.5*(-3)*(6² - 4²) = 30.

We see that the work used to stretch a spring from 2 cm to 4 cm is equal to work needed to spring from 4 cm to 6 cm, cause the extension is the same in both cases.

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