Finding the change in weight from the force & difference in height (y)

[Ella1777]

Information Given:In 1956, Frank Lloyd Wright proposed the construction of a mile-high building in Chicago. Suppose the building had been constructed.

Question: Ignoring Earth's rotation, find the change in your weight if you were to ride an elevator from the street level, where you weigh 708 N, to the top of the building.

Attempt:
earth's radius is: 4000m
w=708N*(4000/4001)^2=707.6461327N
(since there is a difference by a mile high)
Then I take this and subtract it from the original weigh
708-707.6461327=0.3538673

 

[Orodruin]

Then I take this and subtract it from the original weigh
708-707.6461327=0.3538673

Your approach is fine, but you need to write out the units and not use too many significant digits. Also, note the following:

earth's radius is: 4000m

The unit m is typically reserved for the SI unit meter and the Earth radius is certainly not 4000 m. The non-SI unit mile is typically abbreviated mi.

 

[Ella1777]

Your approach is fine, but you need to write out the units and not use too many significant digits. Also, note the following:The unit m is typically reserved for the SI unit meter and the Earth radius is certainly not 4000 m. The non-SI unit mile is typically abbreviated mi.

I forgot to put my units on this post but I already have the correct units on my homework the units are not my concern since I understand them get it right the majority of the time.
As far as significant digits goes I have to write it all out our professor has stated that it’s the root of the cause of many wrong answers. I put my final answer in my homework as 0.354 (since it is 3 sig figs and sig figs applies to the final answer) Does that mean earth’s radius is 4000mi and I must convert that meters??

Thank you!

 

[jbriggs444]

Does that mean earth’s radius is 4000mi and I must convert that meters??

The figure for the Earth's radius is indeed 4000 mi. But there is no need to convert to meters. You also have the building height in miles. Working in miles and obtaining a dimensionless distance ratio of 4001/4000 is perfectly appropriate.

Can you justify the use of three significant digits in the answer?

 

[Ella1777]

The figure for the Earth's radius is indeed 4000 mi. But there is no need to convert to meters. You also have the building height in miles. Working in miles and obtaining a dimensionless distance ratio of 4001/4000 is perfectly appropriate.

Can you justify the use of three significant digits in the answer?

The answer typed into Wileyplus must be 3 significant figures which rounds to 0.354 but only the final answer applies significant figures all the other work has to include all the digits