A wire suspended vertically from one of its ends stretched by attaching weight of 200 N tothe lower end. The weight stretches the wire by 1 mm. Then the elastic energy stored in the wire is ?

To find the elastic energy stored in the wire when it is stretched by a weight of 200 N, we can use the formula for elastic potential energy. This energy is stored in the wire due to its deformation when it is stretched. The formula to calculate the elastic potential energy (E) in a stretched wire is given by:

Formula for Elastic Potential Energy

The formula is:

• E = 0.5 × F × x

Where:

• E = elastic potential energy
• F = force applied (in Newtons)
• x = extension (in meters)

Substituting Known Values

In this scenario:

• The force (F) applied is 200 N.
• The extension (x) is 1 mm, which we need to convert to meters for our calculations. Since 1 mm = 0.001 m, we have:

x = 0.001 m

Calculating the Elastic Potential Energy

Now we can substitute these values into the formula:

• E = 0.5 × 200 N × 0.001 m

Calculating this gives:

• E = 0.5 × 200 × 0.001
• E = 0.1 Joules

Understanding the Result

The elastic energy stored in the wire is 0.1 Joules. This energy is what allows the wire to return to its original length when the weight is removed, assuming it has not reached its elastic limit. This concept is vital in understanding materials and their properties, especially in engineering and physics contexts.

Real-World Application

Elastic potential energy is not only significant in wires but also in various applications like springs, rubber bands, and even in structural engineering where materials must withstand forces without permanent deformation.

In summary, the elastic energy stored in the wire when stretched by a 200 N weight is 0.1 Joules. This calculation highlights the principles of elasticity and energy storage in materials, which are fundamental concepts in physics and engineering.