Question

A pendulum bob of mass 50 g is suspended on a string from the ceiling of an elevator which is moving downwards with an acceleration 1.5 ms−2. Draw the free body diagram using the non-inertial frame of reference and determine the tension in the string. (Take g = 10 ms−2) (5)
b) What should be the radius of a space station spinning with an angular speed of 2 rpm such that an astronaut inside the station experiences artificial gravity with g = 10 ms−2?

Answer 1

Answer on Question #65696, Physics / Mechanics | Relativity

A pendulum bob of mass $50\mathrm{g}$ is suspended on a string from the ceiling of an elevator, which is moving downwards with an acceleration 1.5 ms-2. Draw the free body diagram using the non-inertial frame of reference and determine the tension in the string. (Take $\mathrm{g} = 10\mathrm{ms}^{-2}$ )

Solution:

Acceleration $a = 1.5 \, \text{m/s}^2$ (Downward),

Pseudo force $= \mathrm{ma} = -0.05\mathrm{kg}\times 1.5\mathrm{m / s^2} = -0.075\mathrm{N}$ (Upward)

Weight $= \mathrm{mg} = 0.49\mathrm{N}$ (Downward)

Total force on the bob $= 0.5 - 0.075\mathrm{N} = 0.425\mathrm{N}$ (Downwards)

Tension in the string $= 0.425\mathrm{N}$

Answer: 0.425 N

What should be the radius of a space station spinning with an angular speed of 2 rpm such that an astronaut inside the station experiences artificial gravity with $g = 10 \, \text{ms}^{-2}$ ?

Answer:

$\omega = 2 \mathrm{rpm} = 2 \times 2 \pi / 60$ radian/s = $\pi / 15$ rad/s

$a = \omega^2 R$

$g = \omega^2 R$

$R = g / \omega^2 = 10 / (\pi /15)^2 m = 2250 / \pi^2 m\approx 228m$

Answer: 228 m

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