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Engine 1 produces twice the power of engine 2.
If it takes engine 1 the time T to do the work W, how long does it take engine 2 to do the same work?
Express your answer in terms of some of all of the variables T and W.
T2=________________

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]

Eduard22sly

The time taken for engine 2 to do the same amount of work is given by:

T₂ = 2T

Let the power of the 1st engine be P₁

Let the power of the 2nd engine be P₂

Power = Work / time

From the question given above,

Engine 1 produces twice the power of engine 2.

Thus,

P₁ = 2P₂

P₂ = ½P₁

  • Next, we shall determine the power used by engine 1 to do the work in time T.

Work = W

Time (T₁) = T

Power (P₁) =?

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 (P₁) = [tex]\frac{W}{T}\\\\[/tex]

Power of engine 2 (P₂) = ½P₁

Power of engine 2 (P₂) = [tex]\frac{1}{2} (\frac{W}{T}) = \frac{W}{2T}[/tex]

Time (T₂) =?

[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

T₂ = 2T

Therefore, the time taken for engine 2 to do the same amount of work is: T₂ = 2T

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