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The spring constant is equal to 147/13. If the 7.5-kg weight is replaced with a 195-N weight, then the displacement is approximately equal to 17.24 cm.
Spring constant is defined to be force divided by displacement. It is expressed mathematically as k = F/x where k is the spring constant, F is the force, and x is the displacement.
The given spring has a length of 35 centimeters. It then stretches to 41.5 centimeters when a 7.5-kilogram weight is hung from its free end. Suppose that the acceleration of gravity g is equal to 9.8 m/s², m = 7.5 kg, x = 41.5 cm and x₀ = 35 cm. The spring constant is calculated as follows:
k = F/x
k = (m · g) / (x - x₀)
k = (7.5 · 9.8) / (41.5 - 35)
k = 73.5/6.5
k = 147/13
The spring constant is confirmed to be equal to 147/13.
Next, we're going to find the displacement if the force applied is 195 N and the spring constant is 147/13.
k = F/x
147/13 = 195/x
147x = 2,535
x = 845/49
x ≈ 17.24
The displacement is confirmed to be approximately equal to 17.24 cm.
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