2020-12-09T15:10:50-05:00
The spiral spring of a spring balance is 25cm, when 5 hang on it and 30cm long when the wait is 10N. What is the length of the spring if the weight is 3N
1
2020-12-14T07:17:10-0500
W 1 = k ( x 1 − x 0 ) W 2 = k ( x 2 − x 0 ) x 2 − x 0 x 1 − x 0 = W 2 W 1 30 − x 0 25 − x 0 = 10 5 x 0 = 20 c m 5 = k ( 25 − 20 ) k = 1 N c m W_1=k(x_1-x_0)\\W_2=k(x_2-x_0)\\\frac{x_2-x_0}{x_1-x_0}=\frac{W_2}{W_1}
\\\frac{30-x_0}{25-x_0}=\frac{10}{5}\\x_0=20\ cm\\5=k(25-20)\\k=1\frac{N}{cm} W 1 = k ( x 1 − x 0 ) W 2 = k ( x 2 − x 0 ) x 1 − x 0 x 2 − x 0 = W 1 W 2 25 − x 0 30 − x 0 = 5 10 x 0 = 20 c m 5 = k ( 25 − 20 ) k = 1 c m N Thus,
3 = 1 ( x − 20 ) → x = 23 c m 3=1(x-20)\to x=23\ cm 3 = 1 ( x − 20 ) → x = 23 c m
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