The system shown in the figure is in equilibrium. Masses m 1 and m 2 are 2 kg and 8kg respectively. Spring constants k 1 and k 2 are 50 N/m and 70 N/m respectively. If the compression in second spring is 0.5 m. What is the compression in first spring? (Both springs have the same natural length) -
Text Solution
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As the springs are fixed to the horizontal and have the same natural length, hence if one spring is compressed, the other must be expanded. Hence, the compression will be negative.
F.B.D. of m 2 T + F 2 = 80 N
and F 2 = 70 × 0.5 = 35 N
∴ T = 80 – 35 = 45 N
F.B.D. of m l T + F 1 + mg
or 45 = F 1 + 20
or F 1 = 25N
∴ x 1 = 
= 0.5m
∴ Compression in first spring = – 0.5 m
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