A person who weights 715 N steps onto a spring scale in the bathroom, and the spring compress by 0.830 cm. (a) What is the spring constant?
To determine the spring constant, we can use Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement of the spring. Mathematically, this can be represented as:
F = k * x
Where:
F = force exerted by the spring (in Newtons)
k = spring constant (in Newtons per meter)
x = displacement of the spring (in meters)
In this scenario, we know that the force exerted by the spring (F) is equal to the weight of the person, which is 715 N, and the displacement of the spring (x) is 0.830 cm, or 0.0083 m.
Plugging these values into Hooke's Law equation, we have:
715 N = k * 0.0083 m
To solve for k, we rearrange the equation to isolate k:
k = (715 N) / (0.0083 m)
k ≈ 86,145.78 N/m
Therefore, the spring constant is approximately 86,145.78 N/m.