Coefficient of static friction of clothes

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SUMMARY

The discussion focuses on calculating the coefficient of static friction necessary for clothes to remain adhered to the wall of a top-loading washing machine drum during its spin cycle. The washing machine operates at 8.5 cycles per second, resulting in a linear speed of 19 m/s for the clothes. The normal force acting on a damp pair of jeans, weighing 2.0 kg, is calculated to be 2083 N. The participants clarify the importance of understanding the direction of forces and accelerations in determining the static friction required to prevent the clothes from sliding down.

PREREQUISITES
  • Understanding of angular velocity and linear speed calculations
  • Knowledge of normal force and its calculation in rotational systems
  • Familiarity with static friction and its role in preventing motion
  • Basic principles of centripetal acceleration and net forces in circular motion
NEXT STEPS
  • Study the derivation of the coefficient of static friction in rotating systems
  • Learn about centripetal acceleration and its effects on objects in circular motion
  • Explore the relationship between normal force and friction in practical applications
  • Investigate the dynamics of forces acting on objects in a rotating frame of reference
USEFUL FOR

Physics students, mechanical engineers, and anyone interested in understanding the dynamics of rotating systems and the forces involved in everyday appliances like washing machines.

tquiva
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Problem:
A top-loading washing machine has a spin cycle that rotates at 8.5 cycles per second. The spinning drub that holds the clothes has a radius of 35 cm.
What is the linear speed of the clothes?
ω = (8.5 cycles/s) / (2pi rad) = 53.4 rad/s
v = ωr = (53.4 rad/s) * (0.35 m ) = 19 m/s

A damp pair of jeans has a mass of 2.0 kg. What is the magnitude of the normal force acting on the jeans by the wall of the drums as it spins?
ΣFy = may
Fn - mg = (mv^2) / (r) = ... = 2083 N

What is the minimum coefficient of static friction necessary so that the clothes can remain stuck to the middle of the drum wall, and not just slide down to the bottom?

I got stuck here on the last question.
I can't seem to figure out what a is in the x direction. My guess is 0, so the static friction is 0?
But that doesn't sound right. Could someone help me please?
 
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tquiva said:
Problem:
A top-loading washing machine has a spin cycle that rotates at 8.5 cycles per second. The spinning drub that holds the clothes has a radius of 35 cm.
What is the linear speed of the clothes?
ω = (8.5 cycles/s) / (2pi rad) = 53.4 rad/s
v = ωr = (53.4 rad/s) * (0.35 m ) = 19 m/s
yes, looks good!
A damp pair of jeans has a mass of 2.0 kg. What is the magnitude of the normal force acting on the jeans by the wall of the drums as it spins?
ΣFy = may
Fn - mg = (mv^2) / (r) = ... = 2083 N
not good...
What is the minimum coefficient of static friction necessary so that the clothes can remain stuck to the middle of the drum wall, and not just slide down to the bottom?

I got stuck here on the last question.
I can't seem to figure out what a is in the x direction. My guess is 0, so the static friction is 0?
But that doesn't sound right. Could someone help me please?

You seem to be confusing your x and y directions. For the second part, what is the direction of the centipetal acceleration? What is the net force in that direction (normal forces act pependicular to the objects on which they act)?
For part 3, what is the net force in the vertical direction? What is the acceleration in the vertical direction (friction forces beween two contact surfaces act parallel to the plane of the contact surfaces)?
 

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