In order to sail through the frozen Artic Ocean, the most powerful icebreaker ever built was constructed in the former Soviet Union. At the heart of the ship's power plant is a nuclear reactor with a power output of 5.60X10^7 W (5.60 times ten to the power of seven W) How long will it take for this power plant to do 5.35X10^10 J (5.35 times 10 to the power of 10 J) of work?
This is a power=work/time problem and i don't know how to solve it. if you answer please explain how so that i can do the rest on my hw
1 watt = 1 J/second so the power plant of 5.60 x 10^7 watts = 5.60 x 10^7 J/second.
Therefore,
5.60 x 10^7 J/s x ??seconds = 5.35 x 10^10 J. Solve for ?? seconds.
To solve this problem, we'll use the equation: Power (P) = Work (W) / Time (t).
We're given the power output of the nuclear reactor, which is 5.60x10^7 W. We want to find the time it takes for the power plant to do 5.35x10^10 J of work.
To find the time, we rearrange the equation to solve for time:
t = W / P
Let's substitute the given values into the equation:
t = (5.35x10^10 J) / (5.60x10^7 W)
Now, we can simplify:
t = (5.35 / 5.60) x (10^10 / 10^7)
The division of the values without the powers of 10 is:
t = 0.955357142857 x 10^(10 - 7)
And when subtracting the exponents of 10:
t = 0.955357142857 x 10^3
Finally, we have:
t ≈ 955.36 seconds
Therefore, it will take approximately 955.36 seconds for the power plant to do 5.35x10^10 J of work.
Remember to always double-check the significant figures and units in your calculations.