Respuesta :
Answer:
[tex]T_2=\frac{T}{2}[/tex]
Explanation:
Given that engine 1 produces twice the power of engine 2.
Let [tex]P_1[/tex] and [tex]P_2[/tex] be the power of engine 1 and engine2.
So, the power of the engine 2,
[tex]P_2 = 2P_1\cdots(i)[/tex]
As, Work = Power x time,
So, the work, W, done by an engine 1:
[tex]W=P_1\timesT\cdots(ii)[/tex]
The work, W, done by an engine 2:
[tex]W_2=P_2\times T_2\cdots(iii)[/tex]
If the work done by both the engines are the same, then
[tex]W_2=W[/tex]
[tex]\Rightarrow P_2\times T_2=P_1\timesT[/tex] [from (ii) nd (iii)]
[tex]\Rightarrow 2P_1\times T_2=P_1\timesT[/tex] [by using (i)]
[tex]\Rightarrow 2 T_2=T \\\\\Rightarrow T_2=\frac{T}{2}[/tex]
Hence, [tex]T_2=\frac{T}{2}.[/tex]
The time taken for engine 2 to do the same amount of work is given by:
Tâ = 2T
Let the power of the 1st engine be Pâ
Let the power of the 2nd engine be Pâ
Power = Work / time
From the question given above,
Engine 1 produces twice the power of engine 2.
Thus,
Pâ = 2Pâ
Pâ = ½Pâ
- Next, we shall determine the power used by engine 1 to do the work in time T.
Work = W
Time (Tâ) = T
Power (Pâ) =?
Power = Work / time
[tex]P_{1} = \frac{W}{T}\\\\[/tex]
- Finally, we shall determine the time taken for engine 2 to do the same work.
Work = W
Power of engine 1 (Pâ) = [tex]\frac{W}{T}\\\\[/tex]
Power of engine 2 (Pâ) = ½Pâ
Power of engine 2 (Pâ) = [tex]\frac{1}{2} (\frac{W}{T}) = \frac{W}{2T}[/tex]
Time (Tâ) =?
[tex]Power = \frac{Work}{time} \\\\ P_{2} = \frac{W}{T_{2}} \\\\\frac{W}{2T} = \frac{W}{T_{2}} \\\\\frac{1}{2T} = \frac{1}{T_{2}}\\\\[/tex]
Invert
Tâ = 2T
Therefore, the time taken for engine 2 to do the same amount of work is: Tâ = 2T
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