A 56.6kg hiker starts at an elevation of 1270m and climbs to the top of a 2660 peak.
(I know the answers to B and C, I just have a question on A)
A) What is the change in the hikers potential energy?
I took PE=mg(h2-h1) and got (56.5)(9.8)(2660-1270)=769643J
When I checked my work with some problems on the net, I was seeing answers as large as mine and others that only used 4 digits (Like 7696J)
Why are they cutting them down, and shouldn't the unit change if they did? If the unit should change... why?
Your calculation looks good to me, except for the number of significant digits (too many) in the answer.
You may want to review the other answers on the net to see if
1. they use different units (hJ, kJ, etc.)
2. they use scientific notation, like 7696*10²J., thereby trimming on the number of significant digits.
Also, is the hiker's mass 56.5 or 56.6?
Just a typo on my part. The hiker's mass is the same as in my equation: 56.5.
I just looked over the answers again. Most people answered the same as I did. A few of them put in scientific notation, but not like you did. they put 7.6X10^5 which doesn't make sense to me. I like your notation better. Fits the four digits. One person answered it in kJ, but the answer was only three digits long. I think I am going with the four digit scientific notation. It makes the most sense to me.
Thank you very much!
I personally would suggest using powers of 10 that are multiples of three (some call it the engineering notation). This makes for easier interpretation, i.e. thousands, millions, billions, etc.
So
769643J
=769.6*10^3J
=769.6kJ
=0.770*10^6J
etc.
The unit for potential energy is Joules (J), which is a derived unit of energy in the International System of Units (SI). In the equation PE = mgh, where m represents mass, g represents the acceleration due to gravity, and h represents the change in height, the product of mass, gravitational acceleration, and change in height will give you the potential energy in Joules.
When calculating the change in potential energy, it is common practice to round the answer to a certain number of significant figures. The level of precision required depends on the context of the problem and the information given. In the case of the hike, the height difference is given with only three significant figures (2660 - 1270 = 1390). Therefore, using four significant figures (7696 J) is appropriate for the answer.
The reason for rounding to four significant figures is to ensure that the calculated result does not imply a false precision. It means that the height difference is known to within plus or minus one unit of the last digit. If the height difference was given with four significant figures (e.g., 1390.0 m), then it would be appropriate to express the change in potential energy with five significant figures.
In summary, rounding the answer to 7696 J is acceptable because it aligns with the level of precision given in the problem statement (three significant figures). It is important to maintain consistent significant figures throughout calculations to avoid introducing inaccuracies or implying false precision.