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Chapter 5: Problem 55

If a washing machine's drum has a radius of \(25 \mathrm{cm}\) and spins at 4.0 rev/s, what is the strength of the artificial gravity to which the clothes are subjected? Express your answer as a multiple of \(g\).

Short Answer

Expert verified
Answer: The strength of artificial gravity acting on the clothes is approximately 16 times Earth's gravity.

Step by step solution

01

Convert the rotation speed to angular velocity

In order to find the centripetal acceleration, we need to determine the angular velocity (蠅) of the drum. We are given the rotation speed in revolutions per second (rev/s), so we'll need to convert this to radians per second (rad/s). The conversion factor is \(2\pi\) radians per revolution. Thus, the angular velocity is: $$ 蠅 = 4.0\,\text{rev/s}\times 2\pi\,\text{rad/rev} = 8\pi\,\text{rad/s} $$
02

Calculate the centripetal acceleration

Now that we have the angular velocity, we can find the centripetal acceleration, which is given by the formula: $$ a_c = 蠅^2 \cdot r $$ where \(a_c\) is the centripetal acceleration, \(蠅\) is the angular velocity, and \(r\) is the radius of the drum. Plugging in our values, we get: $$ a_c = (8\pi\,\text{rad/s})^2 \times 0.25\,\text{m} 鈮� 157.08\,\text{m/s}^2 $$
03

Express the centripetal acceleration as a multiple of \(g\)

To express the artificial gravity acting on the clothes as a multiple of Earth's gravity (\(g \approx 9.81\,\text{m/s}^2\)), we simply divide the centripetal acceleration by \(g\): $$ \frac{a_c}{g} \approx \frac{157.08\,\text{m/s}^2}{9.81\,\text{m/s}^2} 鈮� 16.01 $$ Therefore, the strength of artificial gravity acting on the clothes is approximately 16 times Earth's gravity.

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Most popular questions from this chapter

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