Question

It is weigh-in time for the local under-85-kg rugby team. The bathroom scale used to assess eligibility can be described by Hooke’s law and is depressed 0.75 cm by its maximum load of 120 kg.

(a) What is the spring’s effective spring constant?

a) 160 N/m
b) 213.33 N/m
c) 266.67 N/m
d) 320 N/m

Answer 1

The spring's effective spring constant is 156800 N/m.

Step-by-step explanation:

The spring's effective spring constant can be determined using Hooke's law formula, which states that the force exerted by a spring is proportional to its displacement. The formula for Hooke's law is F = -kx, where F is the force, k is the spring constant, and x is the displacement of the spring.

In this case, the spring is depressed by 0.75 cm (or 0.0075 m) due to the maximum load of 120 kg. We can rearrange the formula to solve for the spring constant: k = -F/x.

1. First, we need to calculate the force applied on the spring. The force can be calculated using the equation F = mg, where m is the maximum load (120 kg) and g is the acceleration due to gravity (approximately 9.8 m/s^2). F = 120 kg * 9.8 m/s^2 = 1176 N.
2. Next, we can substitute the values into our rearranged formula to find the spring constant: k = -1176 N / 0.0075 m = -156800 N/m.
3. Since the spring constant is negative, we need to take the absolute value to get the effective spring constant: |k| = 156800 N/m.

So, the spring's effective spring constant is 156800 N/m.