How to determine the spring constant

Summary

In this video, the speaker explores the calculation of the spring constant using Hooke's Law. A spring is hung from a roof with a mass attached, and the initial and stretched lengths are provided. By analyzing the forces acting on the mass, the relationship between the spring's extension and the force applied is established. The speaker calculates the spring constant and demonstrates how it changes when the mass is doubled. This engaging explanation combines theory with practical examples, making complex physics concepts accessible and understandable.

Takeaways

• 😀 Hooke's Law states that the force exerted by a spring is proportional to its displacement from the equilibrium position.
• 🧮 The formula for Hooke's Law is F = K * x, where F is the restoring force, K is the spring constant, and x is the displacement.
• 📏 To determine the spring constant (K), you need to measure the original and stretched lengths of the spring.
• ⚖️ The equilibrium condition for the spring and mass setup involves balancing the restoring force of the spring with the gravitational force acting on the mass.
• 🧑‍🔬 In the example, the original length of the spring was 8 cm, and the stretched length was 12 cm when a 2 kg mass was applied.
• 🔍 The displacement (x) of the spring is calculated as the difference between the stretched length and the original length.
• 🔢 To calculate K, use the formula K = (M * g) / x, where M is the mass and g is the acceleration due to gravity.
• 🧱 After performing the calculations, the spring constant K was found to be 490 N/m.
• 📈 When the mass is doubled, the stretched length of the spring can be recalculated using the new mass in the previous formula.
• 📐 With a new mass of 4 kg, the new stretched length of the spring was determined to be 16 cm, showing how mass affects spring displacement.

Q & A

What is the main concept being demonstrated in the script?

The script demonstrates the calculation of the spring constant (K) using Hooke's Law, which relates the force exerted by a spring to its displacement.

What are the given measurements for the spring in the scenario?

The initial length of the spring (Li) is 8 centimeters, the stretched length (L stretch) is 12 centimeters, and the mass (M) added to the spring is 2 kilograms.

How is the spring constant (K) calculated in this context?

The spring constant (K) is calculated using the formula K = mg / X, where m is the mass, g is the acceleration due to gravity, and X is the displacement of the spring (L stretch - Li).

What is the value of acceleration due to gravity used in the calculations?

The acceleration due to gravity (g) is taken as 9.8 m/s².

What are the SI unit conversions for the lengths provided?

The initial length Li is converted from 8 centimeters to 0.08 meters, and the stretched length L stretch is converted from 12 centimeters to 0.12 meters.

What is the calculated value of the spring constant (K) based on the provided data?

The calculated value of the spring constant (K) is 494 N/m.

What happens to the spring constant (K) if the mass is doubled?

If the mass is doubled, the script shows that the new length of the spring can be recalculated, but the spring constant (K) itself remains unchanged as it is a property of the spring.

How is the new stretched length of the spring calculated when the mass is doubled?

The new stretched length (L stretch) is calculated using the formula L stretch = (2mg / K) + Li, incorporating the doubled mass and previously calculated K.

What is the final result for the stretched length when the mass is doubled?

The final result for the stretched length when the mass is doubled is 0.16 meters.

Can the stretched length be intuitively estimated based on initial observations?

Yes, based on initial observations, it can be reasoned that if one mass causes a 4-centimeter stretch, then two masses would double that stretch to another 4 centimeters, leading to a total of 16 centimeters (0.16 meters).