Question

The spring of a spring balance is 6.0 in. long when there is no weight on the balance, and it is 8.3 in. long with 9.0 lb hung from the balance. How much work is done in stretching it from 6.0 in. to a length of 12.2 in.

Answer 1

Answer:

74.958 lb-in

Step-by-step explanation:

We are given that

Natural length of spring=l=6 in

After stretching, the length of  spring=8.3 in

Weight=W=9 lb

Extension in the sprig=8.3-6=2.3 in

By hook's law

$F==W=kx$

Using the formula

$9=k(2.3)$

$k=\frac{9}{2.3}=3.9 lb/in$

Extension in the spring when the length of spring after stretching to 12.2 in=12.2-6=6.2 in

Work done, W=$\int_{0}^{6.2}3.9xdx$

$W=[\frac{3.9x^2}{2}]^{6.2}_{0}$

$W=3.9\times \frac{(6.2)^2}{2}$

$W=74.958 lb-in$