A load of 47 N attached to a spring that is
hanging vertically stretches the spring 0.22 m.
What is the spring constant?
To find 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.
Hooke's Law can be expressed as F = -kx, where F is the force exerted by the spring, k is the spring constant, and x is the displacement of the spring.
In this case, we know that the force exerted by the spring is 47 N, and the displacement of the spring is 0.22 m. We can substitute these values into Hooke's Law and solve for k.
47 N = -k * 0.22 m
To isolate the spring constant, divide both sides of the equation by -0.22 m:
k = -47 N / 0.22 m
Now we can calculate the spring constant:
k ≈ -213.6364 N/m
Note that the negative sign indicates that the force exerted by the spring is in the opposite direction of the displacement. However, the spring constant is typically expressed as a positive value, so we can drop the negative sign:
k ≈ 213.6364 N/m
Therefore, the spring constant is approximately 213.6364 N/m.