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ad-work [718]
3 years ago
5

Two flywheels of negligible mass and different radii are bonded together and rotate about a common axis (see below). The smaller

flywheel of radius 21 cm has a cord that has a pulling force of 50 N on it. What pulling force (in N) needs to be applied to the cord connecting the larger flywheel of radius 34 cm such that the combination does not rotate
Physics
1 answer:
AveGali [126]3 years ago
6 0

Answer:

The pulling force applied to the cord connecting the larger flywheel is 30.88 N

Explanation:

Given;

the radius of the smaller flywheel, r₁ = 21 cm

force on the cord of the smaller flywheel, F₁ = 50 N

the radius of the larger flywheel, r₂ = 34 cm

The torque on each flywheel is equal, since there is no rotation.

τ = Fr

where;

τ is torque on each flywheel

F is the force on the cord of each flywheel

r is the radius of each flywheel

F₁r₁ = F₂r₂

F_2 = \frac{F_1r_1}{r_2} \\\\F_2 = \frac{50*0.21}{0.34} \\\\F_2 = 30.88 \ N

Therefore, the pulling force applied to the cord connecting the larger flywheel is 30.88 N

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Answer:

Approximately \rm 11.2 \; N \cdot kg^{-1} at that distance from the center of the planet.

Option A) The low value of g near the cloud top of Saturn is possible because of the low density of the planet.

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The value of g on a planet measures the size of gravity on an object for each unit of its mass. The equation for gravity is:

\displaystyle \frac{G \cdot M \cdot m}{R^2},

where

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  • M is the mass of the planet, and
  • m is the mass of the object.

To find an equation for g, divide the equation for gravity by the mass of the object:

\displaystyle g = \left.\frac{G \cdot M \cdot m}{R^2} \right/\frac{1}{m} = \frac{G \cdot M}{R^2}.

In this case,

  • M = 5.68\times 10^{26}\; \rm kg, and
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Calculate g based on these values:

\begin{aligned} g &= \frac{G \cdot M}{R^2}\cr &= \frac{6.67\times 10^{-11}\; \rm N \cdot kg^{-2} \cdot m^2\times 5.68\times 10^{26}\; \rm kg}{\left(5.82\times 10^7\; \rm m\right)^2} \cr &\approx 11.2\; \rm N\cdot kg^{-1} \end{aligned}.

Saturn is a gas giant. Most of its volume was filled with gas. In comparison, the earth is a rocky planet. Most of its volume was filled with solid and molten rocks. As a result, the average density of the earth would be greater than the average density of Saturn.

Refer to the equation for g:

\displaystyle g = \frac{G \cdot M}{R^2}.

The mass of the planet is in the numerator. If two planets are of the same size, g would be greater at the surface of the more massive planet.

On the other hand, if the mass of the planet is large while its density is small, its radius also needs to be very large. Since R is in the denominator of g, increasing the value of R while keeping M constant would reduce the value of g. That explains why the value of g near the "surface" (cloud tops) of Saturn is about the same as that on the surface of the earth (approximately 9.81\; \rm N \cdot kg^{-1}.

As a side note, 5.82\times 10^7\rm \; m likely refers to the distance from the center of Saturn to its cloud tops. Hence, it would be more appropriate to say that the value of g near the cloud tops of Saturn is approximately \rm 11.2 \; N \cdot kg^{-1}.

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