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Readme [11.4K]
2 years ago
5

As an object slides across a rough horizontal

Physics
1 answer:
tiny-mole [99]2 years ago
6 0

When the object slides across the rough surface some of its potential energy will be lost to friction.

<h3>Conservation of mechanical energy</h3>

The law of conservation of mechanical energy states that the total mechanical energy of an isolated system is always constant.

M.A = P.E + K.E

When the object slides across the rough surface, some of the potential energy of the object will be converted into kinetic energy while the remaining potential energy will be converted into thermal energy due to frictional force of the rough surface.

P.E = K.E + thermal energy

Learn more about conservation of energy here: brainly.com/question/166559

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How many revolutions per minute would a 23 m -diameter Ferris wheel need to make for the passengers to feel "weightless" at the
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Answer:

Approximately 6.2\; {\rm rpm}, assuming that the gravitational field strength is g = 9.81\; {\rm m\cdot s^{-2}}.

Explanation:

Let \omega denote the required angular velocity of this Ferris wheel. Let m denote the mass of a particular passenger on this Ferris wheel.

At the topmost point of the Ferris wheel, there would be at most two forces acting on this passenger:

  • Weight of the passenger (downwards), m\, g, and possibly
  • Normal force F_\text{normal} that the Ferris wheel exerts on this passenger (upwards.)

This passenger would feel "weightless" if the normal force on them is 0- that is, F_\text{normal} = 0.

The net force on this passenger is (m\, g - F_\text{normal}). Hence, when F_\text{normal} = 0, the net force on this passenger would be equal to m\, g.

Passengers on this Ferris wheel are in a centripetal motion of angular velocity \omega around a circle of radius r. Thus, the centripetal acceleration of these passengers would be a = \omega^{2}\, r. The net force on a passenger of mass m would be m\, a = m\, \omega^{2}\, r.

Notice that m\, \omega^{2} \, r = (\text{Net Force}) = m\, g. Solve this equation for \omega, the angular speed of this Ferris wheel. Since g = 9.81\; {\rm m\cdot s^{-2}} and r = 23\; {\rm m}:

\begin{aligned} \omega^{2} = \frac{g}{r}\end{aligned}.

\begin{aligned} \omega &= \sqrt{\frac{g}{r}} \\ &= \sqrt{\frac{9.81\; {\rm m \cdot s^{-2}}}{23\; {\rm m}}} \\ &\approx 0.653\; {\rm rad \cdot s^{-1}} \end{aligned}.

The question is asking for the angular velocity of this Ferris wheel in the unit {\rm rpm}, where 1\; {\rm rpm} = (2\, \pi\; {\rm rad}) / (60\; {\rm s}). Apply unit conversion:

\begin{aligned} \omega &\approx 0.653\; {\rm rad \cdot s^{-1}} \\ &= 0.653\; {\rm rad \cdot s^{-1}} \times \frac{1\; {\rm rpm}}{(2\, \pi\; {\rm rad}) / (60\; {\rm s})} \\ &= 0.653\; {\rm rad \cdot s^{-1} \times \frac{60\; {\rm s}}{2\, \pi\; {\rm rad}} \times 1\; {\rm rpm} \\ &\approx 6.2\; {\rm rpm} \end{aligned}.

3 0
1 year ago
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