Dimensional Analysis and units of time

In summary: Here's a revised version:##v = \frac{1 ~ light~minute}{1 ~ minute} = 1 ~ light~minute ~ per~minute####t = \frac{1 ~ light~minute}{1 ~ light~minute ~ per~minute} = 1 ~ minute####t = \frac{1~c}{1 ~ light~minute ~ per~minute} = \frac{1~c}{1} = c = 1 ~ light~minute ~ per~minute##So the speed of light in this system is 1 light minute per minute.
  • #1
gtguhoij
33
2
Homework Statement
If someone is using the minute as their unit of time, what unit should they choose for length so the speed of light will be one in those units?
Relevant Equations
Dimensional Analysis
time = x(min)
distance = 1(y)
y = unknown unitsI think the answer should be 1(y)/ Min. This is not correct becase 1(y) is unknown. Any help?

I have the answer but am confused
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  • #2
How far does light travel in one minute?
 
  • #3
A light minute.
 
  • #4
gtguhoij said:
A light minute.
Is that a unit of distance, then?
 
  • #5
I think so but from your question it seems it is not. Why is it not?
Do you mean something like 17,987,547,480.00 meters/minutes? except it is = 1 y/minutes?
Where y is an unknown unit of distance.
But how do I make y/minutes = 1 for velocity of light?

I am sorry I am just confused.
 
  • #6
gtguhoij said:
I think so but from your question it seems it is not. Why is it not?
A question is a question. A question is not a statement.

Is a light minute a unit of distance?
 
  • #7
Yes
 
  • #8
gtguhoij said:
Yes
And if you measure distance in light minutes and time in minutes, what is the numerical value of the speed of light in those units?
 
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  • #9
gtguhoij said:
1 light minute.
That has the wrong dimensions for speed. Speed has dimensions of ##LT^{-1}##.
 
  • #10
Let‘s try a different approach. You are trying to convert to a new unit of velocity (nuv) which has magnitude 1. It is given that the new unit of time (nut) is 1 minute. You are trying to figure out the new unit of distance (nud). In these units, velocity is measured in nud’s per minute. The question is how many ft are in a nud so that when you convert the speed of light from ft/ns to nud’s/min you get 1 nud/min.
 
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  • #11
PeroK said:
And if you measure distance in light minutes and time in minutes, what is the numerical value of the speed of light in those units?

Whoops I calculated time and velocity.

##d = vt##
##t = d/v = ##

##v = \frac {186 000 miles }{second} * \frac {60 sec}{1 min} = \frac{111 600 000 mile} {min} ##

## t = \frac {1L ~Min} {11 160 000 ~miles~min} = ##
##\frac {1c} {1116000~miles~min } =## ##\frac {186 000~ miles} {11160000miles~min } = 0.0166 min##
My one question is shouldn't it be ## \frac {0.0166} {min}##. How do I move the minutes units to the top? I am pretty sure there is an algbra rule I just can't remember it. I am pretty sure it is different rule then what I used in the first part of ## t = ... ##

I referenced this site rule number 3 for the first step in ##t=...## https://algebrarules.com/.

If I made any mistakes let me know.
 
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  • #12
gtguhoij said:
Whoops I calculated time and velocity.

##d = vt##
##t = d/v = ##

##v = \frac {186 000 miles }{second} * \frac {60 sec}{1 min} = \frac{111 600 000 mile} {min} ##

## t = \frac {1L ~Min} {11 160 000 ~miles~min} = ##
##\frac {1c} {1116000~miles~min } =## ##\frac {186 000~ miles} {11160000miles~min } = 0.0166 min##
My one question is shouldn't it be ## \frac {0.0166} {min}##. How do I move the minutes units to the top? I am pretty sure there is an algbra rule I just can't remember it. I am pretty sure it is different rule then what I used in the first part of ## t = ... ##

I referenced this site rule number 3 for the first step in ##t=...## https://algebrarules.com/.

If I made any mistakes let me know.
I'm lost for words. I have no idea what you are trying to do: ##c = 1## light-minute per minute, by definition.
 
  • #13
This might help...

You do not need to use c = 186,000 miles/second.

An apostrophe is the symbol for 1 foot.
It appears you are told that c = 1’/ns. This means c = 1ft/ns.
So light moves 1 foot each nanosecond (approximately true in a vacuum).

How far (in feet) does light travel in 1 minute?

This distance is the size of the required unit (which you call ‘y’), because light travels a distance ‘y’ in 1 minute. So speed = 1 y/min.

The question simply wants the value of y expressed in feet.
 
  • #14
PeroK said:
I'm lost for words. I have no idea what you are trying to do: ##c = 1## light-minute per minute, by definition.

And in terms of other units: 1 light minute is 60 light seconds. A light second is 299 792 458 meters by definition.

Therefore a light minute is [itex]60 \times 299\,792\,458[/itex] meters.
 
  • #15
I get what to do now to get the correct answer. Is the math correct in post #11? Even though it doesn't answer the question.
 
  • #16
gtguhoij said:
I get what to do now to get the correct answer. Is the math correct in post #11? Even though it doesn't answer the question.
No. One light minute divided by the speed of light equals 1 minute. There’s a typo in the velocity equation (1 too many zeros). In the time equation, the units of velocity in the denominator are wrong and there are issues with your calculated value of a light minute (it looks like you are mixing different time units, seconds and minutes).
 
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Related to Dimensional Analysis and units of time

1. What is dimensional analysis?

Dimensional analysis is a mathematical technique used to convert between different units of measurement. It involves multiplying or dividing by conversion factors to cancel out unwanted units and ensure the final answer is in the desired unit of measurement.

2. Why is dimensional analysis important?

Dimensional analysis is important because it allows scientists to make accurate and consistent measurements by converting between different units of measurement. It also helps to identify and correct errors in calculations by checking the dimensions of the final answer.

3. What are the basic units of time?

The basic units of time are seconds, minutes, hours, days, weeks, months, and years. These units can be converted to each other using dimensional analysis.

4. How do you convert between units of time?

To convert between units of time, you need to use conversion factors. For example, to convert from seconds to minutes, you would multiply the number of seconds by 1 minute/60 seconds. This would cancel out the seconds and leave you with the answer in minutes.

5. Can dimensional analysis be used for all units of measurement?

Yes, dimensional analysis can be used for all units of measurement as long as the conversion factors are known. It is a versatile and widely applicable technique in the field of science and mathematics.

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