It is weigh-in time for the local under 85 kg rugby team. The bathroom scale that is used to assess eligibility can be described by Hooke's law, which is depressed 0.77 cm for its maximum load of 119 kg. What is the scale's effective spring constant k?
143975.31 N/m
Explanation:
Hook's law: Hook's law states that the force applied to an elastic material is directly proportional to its extension, provided that the elastic limit is not exceeded.
From Hook's law,
F = ke Equation 1
Where F = applied force, k = spring constant, e = extension/depression.
Make k the subject of the equation,
k = F/e Equation 2
From the question,
The weight acting on the bathroom scale is the same as the applied force.
F = mg Equation 3
Substitute equation 3 into equation 2
k = mg/e Equation 4
Given: m = 119 kg, e = 0.81 cm = 0.0081 m.
Constant: g = 9.8 m/s²
Substitute into equation 4
k = 119(9.8)/(0.0081)
k = 143975.31 N/m.
Hence the effective spring constant = 143975.31 N/m