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Over [174]
2 years ago
12

A uniform 1.6-kg rod that is 0.89 m long is suspended at rest from the ceiling by two springs, one at each end. Both springs han

g straight down from the ceiling. The springs have identical lengths when they are unstretched. Their spring constants are 31 N/m and 63 N/m. Find the angle that the rod makes with the horizontal.
Physics
1 answer:
artcher [175]2 years ago
4 0

Answer:

8.27°

Explanation:

To angle difference will be determined by the difference in the displacement of the springs, produced by the weight of the center of mass of the rod.

d=y_1-y_2=\frac{F_1}{k_1}-\frac{F_2}{k_2}=\frac{0.5mg}{31N/m}-\frac{0.5mg}{63N/m}\\\\d=0.5(1.6kg)(9.8m/s^2)[\frac{1}{31N/m}-\frac{1}{63N/m}]=0.128m

by a simple trigonometric relation you obtain that the angle:

sin\theta=\frac{d}{l}=\frac{0.128m}{0.89m}=0.144\\\\\theta=sin^{-1}(0.144)=8.27\°

hence, the angle between the rod and the horizontal is 8.27°

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