Errors and uncertainties

 

Rules to perform mathematical operations

 Addition and subtraction/Addition and subtraction

Multiplication and division/Multiplication and division

lg and ln

Uncertainty and errors

Addition and subtraction

Multiplication and division

root, powers, etc

Errors

What is an error?

What is a zero error?

What is a parallax error?

What is the kilowatt-hour?

The kilowatt-hour is the unit in which usage of electricity is measured in the home.

You would remember that the SI unit of energy is the Joule (J)  as you have seen in  work done, gravitational potential energy or kinetic energy.

Now as you know the rating of home appliances is its power and the unit of power is the Watt (W).

Now if a kettle with a rating of 1000 W is used for two hours, then the amount of energy used will be calculated as shown:

Power = Energy used / time taken

Energy used = power * time taken  = 1000 * (2 * 3600)

                    = 7200000 J

                     = 7.2 MW (Megawatt)

However as you can see such calculation is difficult and beyond someone that is not a Physicist.

Hence in order to make matter more simple we use the Kilowatt-hour.

If we use the example above we would need to use the equation below:

Energy used in kilowatt-hour = power of appliance in Kilowatt  x time in hour

Hence the energy used = 2 kW x 2 h

= 4  kilowatt-hour (kWh)

As you can see it is quite simple to determine the the energy used in kilowatt-hour.

What is power?

Power is the rate of doing work.

From the definition we can deduce the following equation

Power = Work done /Time taken

The unit of power is the Watt (symbol W) or the Joule/second (J/s)

Example 1

A boy pushes a box and as a result does 120 J of work in 10 s. What is the power developed by the boy?

Power = Work done / time taken

= 120 /10

= 12 W or J/s

There is another definition for power that is often used. It is

Power is the rate of dissipation of energy or the rate of change of energy conversion.

Power = Energy dissipated / Time taken

Example 2

A girl climbs a staircase gaining 500 J of gravitational potential energy in 10 s.

What is the power developed by the girl?

Power = Energy conversion / Time taken

= 500 / 10

= 50 W or J/s

Example 3

During the boiling of some water 4000 J of heat energy is dissipated in the kettle’s heater in a time of 8 s. What is the power of the heater?

Power = Energy dissipated/Time taken

= 4000/8

= 500 W or J/s

It is now time to do some questions. It will give these questions after a few of you have supplied your answers.

1. A trains of mass 50000 kg accelerated form rest and reaches a velocity of 50 ms^-1 in 60 s.

(a) Calculate the kinetic energy gained by the train.

(b) Calculate the power of the train engine.

2. A lamp is rated 80 W. If it is switched on for two hours, how much light energy is dissipated.