Class 9th
Work And Energy (Power)
Introduction:
If we look at work done , work done doesn’t give any reference to the passage of time . For example, if we lift an object of weight 100N to the height of 1.0 m , so work done will be ,
w = 100 × 1.0
w = 100 J
We have done 100 J of work on the object whether it take 1.0 minute or 10 minutes. Now , if we want to know how quickly work is done we describe this in terms kf power.
- Power:
The rate of doing work is known as power. We can also define it as ‘ Work done per unit time is known as power’.
Mathematical Form:
Power =work done/time
P = w/t
Nature of Quantity:
Like work done power is also a Scaler quantity because it doesn’t need a direction.
We can also define power in terms of Energy.
The rate of transfer of energy is known as Power. Power here describes how quickly energy is transferred from one form to another form.
Mathematically,
Power = Energy/time
P = E/t
Unit of Power:
The unit of power is given by ,
Power = Work / time
Power = Joule / second
Watt = J/s
The S.I unit of power is Watt( in honour of James watt , the first person to invent heat engine, which is equal to Joule per second.
Show that power is dot product of force and velocity?
Answer:
We know that, power is given by ,
P = work / time
P = w/t
As work done is product of force and displacement,
w = F.S
So ,
P = F.s/t
P = F (s/t)
As , velocity= s/t
So ,
P = F(V)
Since force and velocity are both vectors and power is a scaler Quantity so it is dot product of force and velocity.
SLO Question:
How unit of power Watt can be defined?
Watt is equal to Joule / second.
1 Watt = 1J / 1s
- In terms of work :
Power will be one watt if an object does 1 Joule work in 1 second.
- In terms of Energy:
Power will be 1 Watt of an object transfers 1 Joule energy in 1 second.
- Other units of power :
- In British system {FPS} the unit of power is foot-pound per second. (ft.lb/s).
- For practical and commercial purposes, a larger unit of power is used which is horse power (hp).
One horse power is equal to 550 ft.lb/s or 746 watt .
1 hp = 746 watt
A unit of energy (or work ) can be defined in terms of power which is Kilowatt hour(KWh).
- Kilowatt Hour (1KWh):
It is the unit of energy. It is defined as ” Energy consumed by an object of Power 1 kW in one hour “.
We can define kWh in terms of Work done as
” Work done by an object of power 1kW in 1 hour”.
1kWh = 1× 10³× J/s × 3600 s • Watt = J/s
1 kWh = 3600 × 10³ J
1 kWh = 3.6 × 10³ × 10³ J
1 kWh = 3.6 × 10⁶ J
1kWh = 3.6 MJ • Mega = 10⁶
Example 6.5
A crane is capable of doing 1.50× 10⁵ J work in 10.0 s. What is the power of the crane in watts and hp?
Given Data :
Work done = w = 1.50× 10⁵ Joule
Time = t = 10.0 s
Required:
Power = P = ?
Solution:
Since power is given by ,
P = work / time
P = w / t
Putting values ,
P = 1.5 × 10⁵ J / 10.0 s
P = 1.5 × 10⁵ J × 10-1s-1
P = 1.5 × 105-1watt
P = 1.5 × 10⁴ watt
Now to convert power in hp divide it by 746 because 1 hp = 746 watt
P = (1.5×10⁴)/746
P = 20 hp
So the power of an object doing 1.5 × 10⁵ Joule work in 10 seconds will be 1.5 × 10⁴ Watt and 20 hp.
Assignment 6.5
An electric heater is heated at 250 watt. Calculate the amount of heat generated in 10 minutes.
Given Data :
Power =P = 250 watt
Time = t = 10 minutes= 10× 60 = 600 seconds
Required:
Heat energy generated = E = ?
Solution:
As we know that , power in terms of energy can be written as
P = E / t
So , E = P× t
Putting values ,
E = 250 watt × 600 seconds
E = 250 Js-1× 600 s
E = 1,50,000 J
So the amount of heat generated by an electric heater of power 250 watt in 10 Minutes will be 1,50,000 J .
Related Example:
What will be amount of energy consumed by an object of power 1 kW in 1.0 hour?
Given Data:
Power = P = 1kW = 1×10³ watt
Time = t = 1.0 hour = 1× 3600 seconds = 3600 seconds
Required:
Energy= E = ?
Solution:
Power in terms of energy is given by ,
P = E /t
P× t = E
E = P × t
E = 1× 10³ watt × 3600 seconds
E = 3.6 × 10³ × 10³ Joule
E = 3.6 × 10⁶ Joule
E = 3.6 MJ
So the energy of an object of power 1 kW in 1 hour will be 3.6 MJ.
