Calculate the power of an engine in terms of HP which needed to lift 1000kg of coal in 30 minute from coal mine 100m deep (given g =10ms-2)
Answers
Given :
• Mass of coal = 1000 kg
• Time = 30 minutes
• Height = 100 m
To find :
• Power of the engine
Solution :
Here we have to find the peer of the engine. So, firstly we shall convert the time from minutes into seconds.
→ Time = 30 minutes
→ Time = 30 × 60
→ Time = 1800 seconds
Now, by using the formula of power we will get the power of engine in W.
→ Formula to calculate power :-
→ Power = mgh ÷ t
where,
- m = mass
- g = gravity
- h = height
- t = time
we have,
- m = 1000 kg
- g = 10 m/s²
- h = 100 m
- t = 1800 seconds
Substituting the given values :-
→ Power of the engine = 1000 × 10 × 100 ÷ 1800
→ Power of the engine = 1000 × 10 ÷ 18
→ Power of the engine = 555.56
Therefore, power of the engine = 555.56 W
But we need to find the power in HP. So, in order to convert the value from W into HP. Divide it by 745
→ Power = 555.56 ÷ 745
→ Power = 0.745
Therefore, power of the engine in HP = 0.745 HP