To an order of magnitude, through how many revolutions will it turn?

[chocolatelover]

Hi everyone,

Homework Statement

An automobile tire is rated to last for 35,000 miles. To an order of magnitude, through how many revolutions will it turn?

Homework Equations

2pir

The Attempt at a Solution

d=3f=.9144m

r=.9144/2
=.4572

n(2pi)r=35,000miles

(35,000miles)=56327040meters

n(2pi)(.4572meters)=56327040meters

409867.3=
409868

Does that look right?

Thank you very much

 

[mezarashi]

I agree very much that you will need to do:

35,000 miles = (2*pi*r)n

But your last step from
n*2pi*.4572 = 56327040m
n = 409868 ? appears wrong, simply from putting those numbers into the calculator.

 

[D H]

An automobile tire is rated to last for 35,000 miles. To an order of magnitude, through how many revolutions will it turn?
...
409867.3=
409868

Does that look right?

No. First, you did something wrong. Second, your incorrect answer has too many digits. The question asks for the answer to an order of magnitude.

Work out the answer correctly to however many digits you want. After that, I will (or someone else) will show you how to calculate it to do these order of magnitude calculations.

 

[chocolatelover]

Thank you very much

n*2pi*.4572 = 56327040m
n(2.872672322)=56327040m
n=1960788.899

Does that look right?

Could someone please show me how to convert it to the order of magintude?

Would that just be 1.96 X 10^6

 

[D H]

The term order of magnitude means 1, 10, 100, etc. In other words, less than one significant digit. You are still using three significant digits.

Now that you have the correct numerical answer, here is an easy way to compute a rough estimate of the answer

$$N=\frac{l}{\pi d} = \frac{35000\,\text{miles}}{3\pi\,\text{feet}}$$

The first thing to recognize is that $3\pi$ feet is about 10 feet. After converting 35,000 miles to feet all we have to do is divide by 10. Multiplying 35,000 by 5,280 is a pain in the rear. Multiplying 30,000 by 6,000 is a lot easier, and will be close to correct:

$$(3*10^4)*(6*10^3) = 18*10^7 \approx 2*10^8$$

Dividing by 10 gives 20 million, which is correct to within an order of magnitude. (Actually, its even better than that; this is correct to one decimal place.)

 

[chocolatelover]

Thank you very much

Regards