The Relationship Between Work and Spring Stretching

Oct 13, 2025 by miodeya.com 147 views

**If 13.2 J of work are performed in stretching an ideal spring with a spring constant (force constant) of 2500 N/m, by what distance is the spring stretched? Answer in units of cm.**

Understanding the Problem

Before we dive into the solution, let's break down the problem and understand what's being asked. We're given an ideal spring with a spring constant (force constant) of 2500 N/m, and we're told that 13.2 J of work is performed in stretching the spring. Our goal is to find the distance by which the spring is stretched.

The Relationship Between Work and Spring Stretching

To solve this problem, we need to understand the relationship between work and spring stretching. When a spring is stretched, it stores energy in the form of elastic potential energy. The amount of energy stored in the spring is directly proportional to the distance by which it is stretched. Mathematically, this can be represented by the equation:

W = (1/2)kx^2

where W is the work done in stretching the spring, k is the spring constant, and x is the distance by which the spring is stretched.

Solving for Distance

Now that we have the equation, we can solve for the distance by which the spring is stretched. We're given that W = 13.2 J and k = 2500 N/m. Plugging these values into the equation, we get:

13.2 = (1/2)(2500)x^2

To solve for x, we can start by multiplying both sides of the equation by 2 to get rid of the fraction:

26.4 = 2500x^2

Next, we can divide both sides of the equation by 2500 to isolate x^2:

0.01056 = x^2

Finally, we can take the square root of both sides of the equation to solve for x:

x = √(0.01056) = 0.103 cm

Conclusion

Therefore, the spring is stretched by a distance of 0.103 cm.

Frequently Asked Questions

Q: What is the spring constant (force constant) of the ideal spring?

A: The spring constant (force constant) of the ideal spring is 2500 N/m.

Q: How much work is performed in stretching the spring?

A: 13.2 J of work is performed in stretching the spring.

Q: What is the distance by which the spring is stretched?

A: The spring is stretched by a distance of 0.103 cm.

Q: What is the relationship between work and spring stretching?

A: The amount of energy stored in the spring is directly proportional to the distance by which it is stretched.

Q: How can we solve for distance in the equation W = (1/2)kx^2?

A: We can solve for distance by plugging in the given values for work and spring constant, and then isolating x^2 and taking the square root of both sides of the equation.

Q: What is the unit of distance in the solution?

A: The unit of distance in the solution is cm.

Q: What type of spring is being used in the problem?

A: An ideal spring is being used in the problem.

Q: What is the equation that represents the relationship between work and spring stretching?

A: The equation that represents the relationship between work and spring stretching is W = (1/2)kx^2.