A wire 4m long 0.3 mm diameter is streteched by a force of 8 kg.wt. If the extension in the length amounts to 1.5 mm, calcualte the energy stored in the wire?

Explanation

To calculate the energy stored in the wire when it is stretched, we can follow these steps:

### Step 1: Identify the given values
- Length of the wire (L) = 4 m
- Diameter of the wire (d) = 0.3 mm = 0.3 × 10^-3 m
- Force (F) = 8 kg weight = 8 × 9.8 N (since weight = mass × gravity)
- Extension in length (ΔL) = 1.5 mm = 1.5 × 10^-3 m

### Step 2: Convert the force into Newtons
To find the force in Newtons:
\[ F = 8 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 78.4 \, \text{N} \]

### Step 3: Calculate the energy stored in the wire
The energy (U) stored in the wire when it is stretched can be calculated using the formula:
\[ U = \frac{1}{2} \times F \times \Delta L \]

Substituting the values we have:
\[ U = \frac{1}{2} \times 78.4 \, \text{N} \times (1.5 \times 10^{-3} \, \text{m}) \]

### Step 4: Perform the calculation
Calculating the energy:
\[ U = \frac{1}{2} \times 78.4 \times 1.5 \times 10^{-3} \]
\[ U = 39.2 \times 1.5 \times 10^{-3} \]
\[ U = 58.8 \times 10^{-3} \, \text{J} \]
\[ U = 0.0588 \, \text{J} \]

### Final Answer
The energy stored in the wire is **0.0588 Joules**.

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