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Suppose that 6 J of work is needed to stretch a spring from its natural length of 28 cm to a length of 43 cm. (a) How much work is needed to stretch the spring from 33 cm to 38 cm

User Wella
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1 Answer

12 votes

Answer:

Workdone = 0.67 Joules

Step-by-step explanation:

Given the following data;

Workdone = 6J

Extension = 43 - 28 = 15cm to meters = 15/100 = 0.15m

The workdone to stretch a string is given by the formula;

Workdone = ½ke²

Where;

k is the constant of elasticity.

e is the extension of the string.

We would solve for string constant, k;

6 = ½*k*0.15²

6 = ½*k*0.0225

Cross-multiplying, we have;

12 = 0.0225k

k = 12/0.0225

k = 533.33N/m

a. To find the workdone when e = 33, 38.

Extension = 38 - 33 = 5 to meters = 5/100 = 0.05m

Workdone = ½*533.33*0.05²

Workdone = 266.67 * 0.0025

Workdone = 0.67 Joules

Therefore, the amount of work (in J) needed to stretch the spring from 33 cm to 38 cm is 0.67.

User DShook
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