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Answer :
(a)The spring constant is approximately 1207.75 N/m. and (b) the length of the spring when the 185 N weight is hung is 36.3 cm
(a) To find the spring constant (in N/m), follow these steps:
1. Calculate the change in length of the spring: ΔL = stretched length - initial length = 27.9 cm - 21.0 cm = 6.9 cm. Convert to meters: ΔL = 0.069 m.
2. Calculate the force exerted by the 8.50 kg mass: F = mg = (8.50 kg)(9.81 m/s^2) = 83.385 N.
3. Use Hooke's Law (F = kΔL) to find the spring constant, k: k = F/ΔL ≈ 83.385 N / 0.069 m = 1207.75 N/m.So, the spring constant is approx 1207.75 N/m.
(b) To find the length of the spring (in cm) when the 8.00 kg weight is replaced with a 185 N weight, follow these steps:
1. Calculate the new change in length using Hooke's Law: ΔL = F/k = 185 N / 1207.75 N/m ≈ 0.153 m.
2. Convert ΔL to centimeters: ΔL = 15.3 cm.
3. Add the initial length to the new change in length: L = initial length + ΔL = 21.0 cm + 15.3 cm = 36.3 cm.So, the length of the spring is 36.3 cm.
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