GCSE Physics Tutorial - Calculating Spring Constant from Hooke's Law
Hooke's law describes the relationship between the force applied to a spring and the resulting extension or compression of the spring. It states that the force needed to extend or compress a spring is directly proportional to the change in length produced. Mathematically, Hooke's law can be expressed as:
F = k × ΔL
where F is the force applied to the spring, k is the spring constant (also known as the stiffness constant), and ΔL is the change in length (extension or compression) of the spring.
Calculating the Spring Constant (k): To calculate the spring constant, you need to know the force applied to the spring (F) and the corresponding change in length (ΔL). Follow these steps to find the spring constant:
Measure the force (F): Use a force meter or spring balance to measure the force applied to the spring. Make sure to measure in newtons (N), the unit of force.
Measure the change in length (ΔL): Determine the change in length of the spring when the force is applied. Measure this in meters (m).
Apply Hooke's law equation: Substitute the values of force (F) and change in length (ΔL) into Hooke's law equation.
Solve for the spring constant (k): Divide the force (F) by the change in length (ΔL) to find the spring constant.
Example: Let's consider an example where a force of 10 N is applied to a spring, and it produces a change in length of 0.05 m.
Step 1: Measure the force (F) = 10 N Step 2: Measure the change in length (ΔL) = 0.05 m Step 3: Apply Hooke's law equation: F = k × ΔL Step 4: Solve for the spring constant (k): k = F / ΔL = 10 N / 0.05 m = 200 N/m
Calculating the spring constant using Hooke's law is straightforward and involves measuring the force applied to the spring and the resulting change in length. By knowing the spring constant, you can understand how stiff or flexible a spring is and use this information in various engineering and physics applications, such as designing mechanical systems or analysing the behaviour of materials under load.
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