Key Concept: Friction, Real-World Application
b) 300,000 J
[Solution Description]
First, calculate the total energy lost due to friction. The machine loses 500 J every minute, so in 2 hours (120 minutes), the energy lost is:
$500 \, \text{J/min} \times 120 \, \text{min} = 60,000 \, \text{J}$
Since the efficiency of the machine is 80\%, the energy input must compensate for the energy lost and also provide the useful energy. Let $E_{\text{input}}$ be the total energy input. Then:
$0.8 \times E_{\text{input}} = E_{\text{input}} - 60,000$
Solving for $E_{\text{input}}$:
$0.2 \times E_{\text{input}} = 60,000 \\ \\ E_{\text{input}} = \frac{60,000}{0.2} = 300,000 \, \text{J}$
Therefore, the total energy input required is 300,000 J.
Your Answer is correct.
b) 300,000 J
[Solution Description]
First, calculate the total energy lost due to friction. The machine loses 500 J every minute, so in 2 hours (120 minutes), the energy lost is:
$500 \, \text{J/min} \times 120 \, \text{min} = 60,000 \, \text{J}$
Since the efficiency of the machine is 80\%, the energy input must compensate for the energy lost and also provide the useful energy. Let $E_{\text{input}}$ be the total energy input. Then:
$0.8 \times E_{\text{input}} = E_{\text{input}} - 60,000$
Solving for $E_{\text{input}}$:
$0.2 \times E_{\text{input}} = 60,000 \\ \\ E_{\text{input}} = \frac{60,000}{0.2} = 300,000 \, \text{J}$
Therefore, the total energy input required is 300,000 J.
