A machine tool receives an input power of
1
2
kW
.
If mechanical losses are
1
8
%
,
calculate the useful output power.explain in detail

Question

A machine tool receives an input power of 
1
2
 ﻿kW
.
If mechanical losses are 
1
8
%
,
calculate the useful output power.explain in detail

VIPSolutions · Accepted Answer

# Calculation of Useful Output Power

Given:

- **Input power** ($ P_{in} $) = 12 kW
- **Mechanical losses** = 18%

## Step 1: Calculate Mechanical Losses (in kW)

Mechanical losses represent the portion of input power lost due to friction, heat, etc., and not available as useful output.

$$
\text{Mechanical losses} = \frac{18}{100} \times 12 \text{ kW}
$$
$$
= .18 \times 12 \text{ kW}
$$
$$
= 2.16 \text{ kW}
$$

## Step 2: Calculate Useful Output Power

Useful output power is the remaining power after deducting losses from the input.

$$
\text{Useful output power} = \text{Input power} - \text{Mechanical losses}
$$
$$
= 12 \text{ kW} - 2.16 \text{ kW}
$$
$$
= 9.84 \text{ kW}
$$

## Step 3: Final Answer

**The useful output power of the machine tool is:**

$$
\boxed{9.84\ \text{kW}}
$$

---

**Summary Table:**

| Quantity              | Value      |
|-----------------------|------------|
| Input Power ($P_{in}$)        | 12 kW      |
| Mechanical Losses     | 2.16 kW    |
| Useful Output Power   | 9.84 kW    |

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A machine tool receives an input power of 1 2 kW . If mechanical losses are 1 8 % , calculate the useful output power.explain in detail

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