A machine delivers power that is three times its original value, while the duration of operation stays unchanged. How does the work done by the machine change?
It becomes three times larger.
To determine how the work done by the machine changes when its power increases, we begin by understanding the relationship between power, work, and time.
The formula for power (P) is given by:
P = \frac{W}{t}
where:
- W is the work done
- t is the time duration
From this formula, we can rearrange to find the work done:
W = P \cdot t
According to the question, the machine's power becomes three times its original value, but the operation time remains unchanged. Let's denote the original power as P_{0} and the original work done as W_{0}:
W_{0} = P_{0} \cdot t
Now, with increased power, the new power is 3P_{0}. The work done with this new power, while the time remains the same, is:
W_{\text{new}} = 3P_{0} \cdot t
This simplifies to:
W_{\text{new}} = 3(W_{0})
This indicates that the work done by the machine becomes three times larger than the original work done.
Therefore, the correct answer is: It becomes three times larger.
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