A washing machine rated 300 Watt is operated for one hour / day. If the cost of one unit is Rs. 3.00, what will be the cost of the energy to operate a washing machine for the month of March?
Rs. 27.90
Understanding the Washing Machine Energy Cost Problem
This problem asks us to calculate the total electricity cost incurred by operating a washing machine with a specific power rating for a set duration, given the cost per unit of energy.
To solve this, we need to determine the total energy consumed by the washing machine during the specified period and then multiply it by the cost per unit of energy.
Steps to Calculate Energy Cost
We can break down the calculation into these steps:
- Convert the washing machine's power rating from Watts to Kilowatts. Energy consumption is typically measured in kilowatt-hours (kWh), also known as 'units'.
- Calculate the energy consumed by the washing machine in one day.
- Determine the total number of days the washing machine is operated during the month of March.
- Calculate the total energy consumed over the entire month of March.
- Calculate the total cost by multiplying the total energy consumed by the cost per unit.
Calculating Daily Energy Consumption
The power rating of the washing machine is given as 300 Watt.
First, convert Watts to Kilowatts:
\( \text{Power (P)} = 300 \text{ Watt} \)
\( 1 \text{ Kilowatt (kW)} = 1000 \text{ Watt (W)} \)
\( \text{Power (P)} = \frac{300}{1000} \text{ kW} = 0.3 \text{ kW} \)
The washing machine is operated for 1 hour per day.
Energy consumed is calculated using the formula:
\( \text{Energy (E)} = \text{Power (P)} \times \text{Time (t)} \)
Daily energy consumption:
\( E_{\text{daily}} = 0.3 \text{ kW} \times 1 \text{ hour} = 0.3 \text{ kWh} \)
So, the washing machine consumes 0.3 kWh of energy each day.
Calculating Total Energy Consumption for March
The calculation is for the month of March. We need to know the number of days in March.
- Number of days in January: 31
- Number of days in February: 28 or 29 (depending on leap year, but not relevant here)
- Number of days in March: 31
- Number of days in April: 30
- etc.
The month of March has 31 days.
Total energy consumed in March is the daily energy consumption multiplied by the number of days in March:
\( E_{\text{total, March}} = E_{\text{daily}} \times \text{Number of days in March} \)
\( E_{\text{total, March}} = 0.3 \text{ kWh/day} \times 31 \text{ days} \)
\( E_{\text{total, March}} = 9.3 \text{ kWh} \)
The total energy consumed by the washing machine in March is 9.3 kWh.
Calculating the Total Cost
The cost of one unit (1 kWh) of energy is given as Rs. 3.00.
Total cost is the total energy consumed multiplied by the cost per unit:
\( \text{Total Cost} = E_{\text{total, March}} \times \text{Cost per unit} \)
\( \text{Total Cost} = 9.3 \text{ kWh} \times \text{Rs. } 3.00/\text{kWh} \)
\( \text{Total Cost} = \text{Rs. } 27.90 \)
The total cost to operate the washing machine for the month of March is Rs. 27.90.
Summary of Calculations
| Parameter | Value | Unit |
|---|---|---|
| Power (P) | 300 | Watt |
| Power (P) | 0.3 | kW |
| Time per day (t) | 1 | hour |
| Daily Energy (Edaily) | 0.3 | kWh |
| Days in March | 31 | days |
| Total Energy (Etotal, March) | 9.3 | kWh |
| Cost per unit | 3.00 | Rs./kWh |
| Total Cost | 27.90 | Rs. |
Based on the calculations, the cost of energy to operate the washing machine for the month of March is Rs. 27.90.
Important Questions from Conservation of Mechanical Energy
A ball is thrown up at a speed of 2m/s. If g = 10m/s 2, then find the maximum height the ball will reach?
A particle of mass 40 g is thrown vertically upwards with a speed of 10 ms -1 . Find the work done by the force of gravity during the time the particle goes up.
Find the work done by the force of gravity during the time a particle of mass 50 gm goes up on being thrown vertically upwards with a speed of 10 m/s.
A uniform chain of mass m and length l is placed on a smooth horizontal table such that \(\frac{1}{4}\)th of its length is hanging from the edge of the table. The chain slips down. Find the kinetic energy of the chain when half of its length is hanging from the edge of the table.
Which of the following equation is also a special case of the work-energy (WE) theorem? (where a is acceleration, u and v are the initial and final speeds and s the distance traversed.)
