Work done by a Spring - Deriving Elastic Potential Energy

The video tutorial explores the physics of a spring-mass system. It begins with a problem statement involving a 1 kg mass on a spring, leading to questions about the spring constant and work done by the spring. Using Hooke's law, the spring constant is calculated. The tutorial then explains how to determine the work done by the spring using integral calculus, highlighting the concept of elastic potential energy. A graphical representation of Hooke's law is provided, illustrating the relationship between force and displacement. The tutorial concludes with a discussion on the directionality of work and energy in the system.

What is the initial problem presented in the video?

• Determining the spring constant and work done by a spring

• Calculating the speed of a moving car

• Measuring the height of a building

• Finding the mass of an object

According to Hooke's Law, what does the force of a spring depend on?

• The color of the spring

• The speed of the mass

• The temperature of the environment

• The displacement from equilibrium position

How is the spring constant calculated in the video?

• Using the mass and gravitational force

• Using the temperature of the spring

• By measuring the length of the spring

• By counting the number of coils in the spring

Why is the integral method used to calculate the work done by the spring?

• Because it is easier than other methods

• Because the spring force is not constant

• Because the spring force is constant

• Because it does not require any calculations

What is the relationship between work done by the spring and elastic potential energy?

• Work done is twice the elastic potential energy

• Work done is half the elastic potential energy

• Work done is the negative of elastic potential energy

• They are unrelated

What does the area under the Hooke's Law graph represent?

• The speed of the mass

• The elastic potential energy

• The weight of the spring

• The temperature of the spring

Why is the work done by the spring considered negative?

• Because the spring is broken

• Because the force and displacement are in opposite directions

• Because the mass is too heavy

• Because the spring is moving upwards