Calculate the spring constant of a spring using Hooke’s Law. Enter the spring displacement and force on the spring to calculate the spring constant.
Hooke’s Law Formula
The following is hooke’s law formula for determining the spring constant of a spring:
F = -k*x
- Where F is the force (N)
- k is the spring constant (N/m)
- x is the displacement (m) (positive for displacement, negative for compression)
What is a spring constant?
A spring constant is a measure of a springs ability to resist compression and elongation. The higher the spring constant, the harder it is to compress or stretch it. This value is also a measure of elasticity. That is, elasticity is directly related to the force constant. The higher the elasticity, the lower the spring constant. The force and displacement are proportional so if graphed against one another, it would yield a straight line.
Taking another look at the equation above it can be seen that there is a negative sign in the equation. This is to take into account the direction of displacement. Displacement can be positive if the spring is being pulled in tension, or negative if the spring is being compressed.
How to Calculate a spring constant
- First, the formula for hooke’s law must be manipulated to solve for k, the spring constant
To do this, we simply divide both sides by -x. This yields the equation k = -F/x.
- Next, we must measure our first variable
In this case we will first measure the force acting on the spring. In most spring applications this is done directly via a gauge. Sometimes it’s also provided in a problem. For this example we will assume 10 Newtons.
- Next, we must measure the displacement
As is the case with the force, when springs are involved this displacement is almost always measured directly or given in the problem. For this example we will say the displacement is -1 meter, meaning the spring is in compression.
- Finally, enter all of the information into our formula
k = -F/X= -10/-1 = -10. The spring constant 10 N*m.
- Analyze the results
Analyze the results for accuracy and apply whats been learned to future problems.
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