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Alexus [3.1K]
3 years ago
7

A child rolls a ball on a level floor 3.5 m to another child. If the ball makes 12.0 revolutions, what is its diameter?

Physics
1 answer:
Ulleksa [173]3 years ago
3 0

d = linear distance traveled by the ball from one child to another child = 3.5 m

n = number of revolutions of the ball = 12

r = radius of the ball

C = circumference of the ball = ?

circumference of the ball is given as

C = 2πr

we know that :

linear distance traveled = number of revolutions x circumference of ball

d = n x  2πr

d =  2πr n

inserting the values

3.5 = 2 (3.14) (12) r

r = 0.046 m

D = diameter of the ball

diameter is given as

D = 2r

D = 2 (0.046)

D = 0.092 m

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You asked a question.  I'm about to answer it. 
Sadly, I can almost guarantee that you won't understand the solution. 
This realization grieves me, but there is little I can do to change it. 
My explanation will be the best of which I'm capable.


Here are the Physics facts I'll use in the solution:

-- "Apparent magnitude" means how bright the star appears to us.

-- "Absolute magnitude" means the how bright the star WOULD appear
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-- Increasing magnitude means dimmer.
Decreasing magnitude means brighter.
+5 is 10 magnitudes dimmer than -5 .

-- Apparent brightness is inversely proportional to the square
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That's all the Physics.  The rest of the solution is just arithmetic.
____________________________________________________

-- The star in the question would appear M(-5) at a distance of
32.6 light years. 

-- It actually appears as a M(+5).  That's 10 magnitudes dimmer than M(-5),
because of being farther away than 32.6 light years.

-- 10 magnitudes dimmer is ( ⁵√100)⁻¹⁰ = (100)^(-2) .

-- But brightness varies as the inverse square of distance,
so that exponent is (negative double) the ratio of the distances,
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(32.6) · (100)^(1) light years

= (32.6) · (100) light years

=  approx.  3,260 light years .   (roughly 1,000 parsecs)


I'll have to confess that I haven't done one of these calculations
in over 50 years, and I'm not really that confident in my result.
If somebody's health or safety depended on it, or the success of
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