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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 (ω) 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: $$ ω = 4.0\,\text{rev/s}\times 2\pi\,\text{rad/rev} = 8\pi\,\text{rad/s} $$
02

Calculate the centripetal acceleration

Now that we have the angular velocity, we can find the centripetal acceleration, which is given by the formula: $$ a_c = ω^2 \cdot r $$ where \(a_c\) is the centripetal acceleration, \(ω\) is the angular velocity, and \(r\) is the radius of the drum. Plugging in our values, we get: $$ a_c = (8\pi\,\text{rad/s})^2 \times 0.25\,\text{m} ≈ 157.08\,\text{m/s}^2 $$
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 \(g\): $$ \frac{a_c}{g} \approx \frac{157.08\,\text{m/s}^2}{9.81\,\text{m/s}^2} ≈ 16.01 $$ 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

A disk rotates with constant angular acceleration. The initial angular speed of the disk is \(2 \pi\) rad/s. After the disk rotates through \(10 \pi\) radians, the angular speed is \(7 \pi \mathrm{rad} / \mathrm{s} .\) (a) What is the magnitude of the angular acceleration? (b) How much time did it take for the disk to rotate through \(10 \pi\) radians? (c) What is the tangential acceleration of a point located at a distance of \(5.0 \mathrm{cm}\) from the center of the disk?
A pendulum is \(0.800 \mathrm{m}\) long and the bob has a mass of 1.00 kg. When the string makes an angle of \(\theta=15.0^{\circ}\) with the vertical, the bob is moving at \(1.40 \mathrm{m} / \mathrm{s}\). Find the tangential and radial acceleration components and the tension in the string. \([\) Hint: Draw an FBD for the bob. Choose the \(x\) -axis to be tangential to the motion of the bob and the \(y\) -axis to be radial. Apply Newton's second law. \(]\)
A roller coaster car of mass 320 kg (including passengers) travels around a horizontal curve of radius \(35 \mathrm{m}\) Its speed is $16 \mathrm{m} / \mathrm{s} .$ What is the magnitude and direction of the total force exerted on the car by the track?
Verify that all three expressions for radial acceleration $\left(v \omega, v^{2} / r, \text { and } \omega^{2} r\right)$ have the correct dimensions for an acceleration.
A coin is placed on a turntable that is rotating at 33.3 rpm. If the coefficient of static friction between the coin and the turntable is \(0.1,\) how far from the center of the turntable can the coin be placed without having it slip off?
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