A load of 46 N attached to a spring that is
hanging vertically stretches the spring 0.10 m.
What is the spring constant?
Answer in units of N/m
Here is a hint:
F = k X
It's called Hooke's Law.
Solve for k, 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 from its equilibrium position.
Hooke's Law equation: F = -k * x
Where:
F = force exerted by the spring (in Newtons)
k = spring constant (in N/m)
x = displacement from the equilibrium position (in meters)
In this case, the force exerted by the spring is equal to the weight of the load, since it is hanging vertically. Weight is given by the equation W = m * g, where m is the mass and g is the acceleration due to gravity.
Given:
Load (force exerted by the spring) = 46 N
Displacement from equilibrium = 0.10 m
Acceleration due to gravity (g) = 9.8 m/s^2
We can now set up the equation:
46 N = -k * 0.10 m
Next, we solve for the spring constant (k):
Divide both sides of the equation by 0.10 m:
46 N / 0.10 m = -k
460 N/m = -k
Finally, to find the spring constant, we take the negative sign into account:
k = -460 N/m
Therefore, the spring constant is -460 N/m (Note: The negative sign indicates that the spring is being stretched, which is the case when a load is attached to it and hanging vertically.)