Physics book, practice passage pg. 93, Q1
Physics book, practice passage pg. 93, Q1
The solution the book provides for this question does not add up to 16 W, which is states is the correct answer. I understand the dimensional analysis aspect of the problem, but I do not get where the numbers came from. Could you please explain to me if I am missing something that was not shown in this calculation?

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Re: Physics book, practice passage pg. 93, Q1
Thanks for your question!
I think there are two tricky parts here. The first is setting up the dimensional analysis, but it sounds like you understand that part well. The other tricky bit is doing the calculation without a calculator. You'll want to practice mental math and the best advice I can offer is to round liberally! But make sure to keep track of which direction you're rounding so you know where the true answer lies in relation to your estimate.
I'll include units in the below so the numbers have a clearer origin. All of the dimensional analysis leaves us and the rounding leaves us with:
(~0.6kg/1day)(1000g/1kg)(~600cal/1g)(~4J/1cal)(1day/24hr)(1hr/60min)(1min/60sec)
which equals
(0.6kg * 1000g * 600cal * 4J * 1day * 1hr * 1day) / (1day * 1kg * 1g * 1cal * 24hr * 60min * 60sec)
which equals
(0.6 * 1000 * 600 * 4) / (24 * 60 * 60)
which equals
1440000 / 86400, which is roughly equal to 100/6, which is closest to the answer, 16 W
Hope this helps!
I think there are two tricky parts here. The first is setting up the dimensional analysis, but it sounds like you understand that part well. The other tricky bit is doing the calculation without a calculator. You'll want to practice mental math and the best advice I can offer is to round liberally! But make sure to keep track of which direction you're rounding so you know where the true answer lies in relation to your estimate.
I'll include units in the below so the numbers have a clearer origin. All of the dimensional analysis leaves us and the rounding leaves us with:
(~0.6kg/1day)(1000g/1kg)(~600cal/1g)(~4J/1cal)(1day/24hr)(1hr/60min)(1min/60sec)
which equals
(0.6kg * 1000g * 600cal * 4J * 1day * 1hr * 1day) / (1day * 1kg * 1g * 1cal * 24hr * 60min * 60sec)
which equals
(0.6 * 1000 * 600 * 4) / (24 * 60 * 60)
which equals
1440000 / 86400, which is roughly equal to 100/6, which is closest to the answer, 16 W
Hope this helps!