Can You Calculate Time Change Over 40 Centuries?

[AMD ZEN]

This problem is baffling myself and several of my friends in the infamous Physics 152 class... so I give it to you to solve. It was on the homework earlier today, and no one got it. Needless to say, we got 5/6 on the homework as a result. But the problem has been bugging us since. So, I was hoping you may have a solution on how to solve this or setup a function of time to assist in solving this.

The question reads as follows:

Assuming the length of day uniformly increased by .0010 secs per century, calculate the cumulative effect one the measure of time over 40 (fourty) centuries.

I would really appreciate help on this problem guys and girls. Thx in advance!

 

[Tide]

You need to sum the terms in an arithmetic series which is just the average of the first and last term multiplied by the number of terms.

 

[HallsofIvy]

I'm not sure I understand the question but it seems simple. If the length of a day increases by .0010 secs per century then in 40 centuries the length of a day will have increased by 40(0.0010) = 0.04 seconds.

(I would not interpret "cumulative effect" to mean the sum of the lengths of the days.)

 

[tmc]

I think he also meant that since you will have an added 0.04 seconds to your 40 centuries, those 40 centuries would last a little bit longer, and hence you would get slightly more than 0.04 seconds added. Basically, youd need to add the same ratio of 0.001seconds/century to the 0.04 added seconds, and then add it again to this new added time, etc.

Now, this added length would be extremely small and would practically be 0.04 seconds.

 

[HallsofIvy]

I think he also meant that since you will have an added 0.04 seconds to your 40 centuries, those 40 centuries would last a little bit longer, and hence you would get slightly more than 0.04 seconds added. Basically, youd need to add the same ratio of 0.001seconds/century to the 0.04 added seconds, and then add it again to this new added time, etc.

Now, this added length would be extremely small and would practically be 0.04 seconds.

That may well be. However, since a century is defined as 100 years and not a specific number of days (a year itself is defined as the time it takes the Earth to orbit the sun- not a specific number of days) I would think that the length of a day would not matter.

 

[matt grime]

This problem is baffling myself and several of my friends in the infamous Physics 152 class... so I give it to you to solve.

Ah, yes, the infamous Physics 152. We talk about it all the time at work. You'd be amazed just how much anguish that course causes us, we can barely get anything done in the day because of its mere existence. It's even more notorious than econimcs 234, if you ask me.