Answer: 3.65 m
Explanation:
from the question we have
angular speed = 33.3 rpm
coefficient of static friction (μ) = 0.3406
acceleration due to gravity (g) = 9.8 m/s^2
to get how far from the center of the turntable can the coin can be placed without having to slip off we equate the formula for the centrifugal force with the frictional force on the turntable force
mv^2 / r = m x g x μ
v^2 / r = g x μ .......equation 1
where
velocity (v) = angular speed (rads/seconds) x radius
we have to convert the angular speed from rpm to rads/seconds
angular speed (rads/seconds) = (2π / 60 ) x rpm
angular speed (rads/seconds) = ((2 x π) / 60 ) x 33.3 = 3.49 rads/ seconds
now
velocity = 3.49 x r = 3.49r
now substituting the value of velocity into equation 1
v^2 / r = g x μ
(3.49r)^2 / r = 9.8 x 0.3406
12.18 x r = 3.34
r = 3.65 m
Answer:
The Mercalli Intensity Scale measures the intensity of an earthquake by observing its effect on people, the environment and the earth’s surface. The Richter Scale measures the energy released by an earthquake using a seismograph. A base-10 logarithmic scale is obtained by calculating the logarithm of the amplitude of waves recorded by the seismograph.
Explanation:
The answer would be false
Liters
Grams
Degrees Celsius
The other answer choices are from the imperial system
<span>40.7 miles.
For this problem, we want to know the length of the chord created by the line and the circle. So let's first create the equations needed.
The slope intercept equation for a line is:
y = ax + b
the value for a will be the the difference in y divided by the difference in x. We're going from y=61 to y=0 for a chance of -61 and from x=0 to x=62 for a change of 62. So the value of a is
-61/62, giving us the formula
y = -(61/62)x + b
Substituting x = 0, we can calculate b
61 = -(61/62)0 + b
61 = b
So the equation for the line is:
y = -(61/62)x + 61
Now for the equation for the circle. Since the circle is centered at the origin, the equation is:
x^2 + y^2 = 48^2
Now we to calculate the intersections.
y = -(61/62)x + 61
x^2 + y^2 = 48^2
x^2 + (-(61/62)x + 61)^2 = 48^2
x^2 + (3721/3844)x^2 - (3721/31)x + 3721 = 2304
(7565/3844)x^2 - (3721/31)x + 3721 = 2304
(7565/3844)x^2 - (3721/31)x + 1417 = 0
1.968002081x^2 - 120.0322581x + 1417 = 0
And we have a rather ugly quadratic equation which we can solve using the quadratic formula, giving the solutions x = 16.00512574 and x = 44.98681081
Now we need to calculate the y values for those 2 x values.
y = -(61/62)x + 61
y = -(61/62)16.00512574 + 61
y = 45.25302145
y = -(61/62)x + 61
y = -(61/62)44.98681081 + 61
y = 16.73878292
So the 2 endpoints are
(16.00512574, 45.25302145) and (44.98681081, 16.73878292)
The distance between those points can be calculated using the Pythagorean theorem.
sqrt((16.00512574 - 44.98681081)^2 + (45.25302145 - 16.73878292)^2)
= sqrt(-28.98168506^2 + 28.51423853^2)
=
sqrt(839.938069 + 813.0617988)
=
sqrt(1652.999868)
= 40.65710107
And finally, we have the solution of 40.7 miles.</span>