Springs & Hooke's Law - GCSE & A-level Physics (full version)

Summary

This video explains Hooke's Law and its applications to springs, covering key concepts like force, extension, and spring constants. It illustrates how doubling the mass on a spring doubles the extension and introduces the concept of the spring constant (K). The video also demonstrates how to calculate the spring constant, the energy stored in a spring, and how to use graphs for these calculations. Furthermore, it explores the behavior of springs in series and parallel, and briefly touches on Young's Modulus, which extends these principles to all materials.

Takeaways

• 😀 Hooke's Law states that the force applied to a spring is directly proportional to the extension or compression of the spring. This relationship is expressed as F = k * x.
• 😀 The spring constant (k) represents the stiffness of a spring. A higher spring constant means the spring is harder to stretch or compress.
• 😀 The spring constant can be found by dividing force (F) by extension (x) using the formula k = F / x.
• 😀 To find the spring constant from experimental data, plot a graph of force vs. extension and determine the gradient. The gradient represents the spring constant.
• 😀 The energy stored in a spring due to its extension is called elastic potential energy, calculated using the formula E = 1/2 k * x^2.
• 😀 In a spring system connected in series, the overall spring constant is halved, leading to a greater extension for a given force.
• 😀 In a spring system connected in parallel, the overall spring constant is doubled, resulting in a smaller extension for the same force.
• 😀 To measure the spring constant using multiple masses, calculate how far the spring extends for each mass, and use the gradient of the force vs. extension graph.
• 😀 Elastic potential energy is determined by the area under the force vs. extension graph, which is typically a triangle for linear springs.
• 😀 Young's Modulus applies the principles of Hooke's Law to materials, providing a measure of their elasticity and resistance to deformation.
• 😀 It is best to plot a graph of mass vs. extension when determining spring constants, as it simplifies calculations by avoiding the need to convert mass to force directly.

Q & A

What does Hooke's Law describe?

Hooke's Law describes the relationship between the force applied to a spring and its resulting extension. It states that the force is proportional to the extension of the spring, represented as F = k * X, where F is the force, k is the spring constant, and X is the extension.

What is the spring constant (k), and how does it relate to the stiffness of the spring?

The spring constant (k) is a measure of a spring's stiffness. A higher spring constant indicates a stiffer spring, which resists extension more than a spring with a lower constant. It is calculated as the force per unit extension (k = F / X).

How do you experimentally find the spring constant?

The spring constant can be found by applying various masses to a spring, measuring the corresponding extension, and plotting a graph of force (F) against extension (X). The gradient of the line in this graph gives the spring constant (k).

What is the formula for elastic potential energy stored in a spring?

The formula for the elastic potential energy stored in a spring is E = 1/2 * k * X^2, where E is the energy, k is the spring constant, and X is the extension.

What is the difference between springs in series and springs in parallel?

In springs connected in series, the overall extension is doubled and the spring constant is halved (k_total = k / 2). In springs connected in parallel, the overall extension is halved, and the spring constant is doubled (k_total = 2k).

Why is it better to plot a mass vs. extension graph when determining the spring constant?

Plotting mass vs. extension allows you to directly calculate the gradient without needing to convert mass to force first, making it a simpler method. The gradient of this graph, when multiplied by gravitational acceleration (g = 9.8 m/s²), gives the spring constant.

How can you calculate the total spring constant for two springs in parallel?

For two springs in parallel, the total spring constant is the sum of the individual spring constants, effectively doubling the overall spring constant (k_total = 2k). This is because the force is shared between the two springs.

What happens to the extension of a spring when its mass is doubled?

When the mass is doubled, the force on the spring is also doubled, which results in the spring stretching twice as much, assuming the spring behaves according to Hooke’s Law.

What does the area under the force vs. extension graph represent?

The area under the force vs. extension graph represents the elastic potential energy stored in the spring. This energy is calculated as the area of the triangle formed under the graph, which is 1/2 * F * X.

What is Young's Modulus, and how does it relate to Hooke's Law?

Young's Modulus is a measure of the elasticity of a material and describes the relationship between stress (force per unit area) and strain (relative deformation). It extends the ideas from Hooke’s Law to all materials, showing how they deform under stress.