In an automatic clothes drier, a hollow cylinder moves the clothes on a vertical circle (radius r = 0.39 m), as the drawing shows. The appliance is designed so that the clothes tumble gently as they dry. This means that when a piece of clothing reaches an angle of above the horizontal, it loses contact with the wall of the cylinder and falls onto the clothes below. How many revolutions per second should the cylinder make in order that the clothes lose contact with the wall when = 72.0°?
rev
Let's solve for radians per second, w. The number of revs per second is
w/(2 pi)
The clothes fall when the weight component along the direction to the center of the drum equals the centripetal force needed to keep the clothes on the drum. At lower speeds or higher angles, the clothes leave the surface and "tumble"
m r w^2 = m g sin 72
w^2 = g sin 72/r = 2.44
w = 1.56 rad/s
That is about 1/2 rev/s
mr bot
Hello! How can I assist you today?
answer this question
Directions: Using the phrase provided below, write a sentence. THEN label your sentences by writing simple, compound, or complex in parentheses after each one.
Example: attended high school
Sentence using the phrase: My neighbor attended high school with my daughter, so they drove together each morning.
Sentence Type: Compound Sentence
1. liked to write poetry
Sentence using the phrase: _________________________________________________
______________________________________________________________________
Sentence Type: ___________________________
She spent hours in her room because she liked to write poetry.
Sentence Type: Complex Sentence
To determine the number of revolutions per second the cylinder should make, we need to find the angular velocity of the cylinder.
The angular velocity (ω) is defined as the rate at which an object rotates or moves around a central axis, measured in radians per second (rad/s). It is related to the number of revolutions per second (rev/s) by the equation:
ω = 2π * rev/s
Given that the clothes lose contact with the wall of the cylinder when the angle (θ) is 72.0°, we can use this information to find the angular velocity.
To understand the relationship between the angle (θ) and the angular velocity (ω), we can create a force diagram for an object moving in circular motion.
When the clothes lose contact with the wall, the weight of the clothes (mg) provides the centripetal force required for circular motion. This force can be calculated using the equation:
mg * cos(θ) = m * ω^2 * r
Where:
m = mass of the clothes
g = acceleration due to gravity
θ = angle (72.0°)
ω = angular velocity
r = radius of the cylinder (0.39 m)
Simplifying the equation, we have:
cos(θ) = ω^2 * r/g
Substituting the given values, we get:
cos(72.0°) = ω^2 * 0.39/9.8
Now, let's solve for ω by rearranging the equation:
ω^2 = cos(72.0°) * 9.8/0.39
ω = sqrt(cos(72.0°) * 9.8/0.39)
ω ≈ 8.32 rad/s
To find the number of revolutions per second, we can use the equation:
rev/s = ω / (2π)
Substituting the value of ω, we get:
rev/s ≈ 8.32 / (2π)
rev/s ≈ 1.32
Therefore, the cylinder should make approximately 1.32 revolutions per second in order for the clothes to lose contact with the wall when the angle is 72.0°.