Centripetal Force; calculating speed

In summary, the conversation discusses a wet towel of mass 0.65 kg in a washing machine's spin cycle. The towel moves in a horizontal circle with a radius of 26 cm at a frequency of 4.6 Hz. The centripetal force causing the towel's acceleration is discussed, as well as the towel's speed and the magnitude of the centripetal force. Using two equations, the speed of the towel is found to be 7.51 m/s, contradicting the given answer of 3.5 m/s.
  • #1
Macrowave
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Homework Statement


A wet towel, of mass 0.65 kg, travels in a horizontal circle of radius 26cm in the spin cycle of a washing machine. The frequency of rotation is 4.6Hz.

a)Name the force causing the centripetal acceleration. What object exerts that force?
b) What is the speed of the towel?
c) Determine the magnitude of the centripetal force on the towel.

Homework Equations



Fc=4pi^2mrf^2
Fc=(mv^2)/r

The Attempt at a Solution



I tried plugging in the values into the first equation and got 30.69 then i tried putting it into the second equation to solve for velocity but got 3.5 and the answer is 7.5. Someone please help me on this question.
 
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  • #2
Probably some algebra error or arithmetic mistake.

Show us some intermediate steps.
 
  • #3
equations are correct.
 
  • #4
4.6hz means that the towel travels 4.6 of its circumference per second.

v=4.6(2piR)cm/s
=9.2 x 26 x pi cm/s
= 751cm/s
= 7.51m/s
 
  • #5
which is correct answer!
 

What is centripetal force?

Centripetal force is the force that keeps an object moving in a circular path. It is always directed towards the center of the circle and is responsible for constantly changing the direction of the object's velocity.

What are the units for centripetal force?

The units for centripetal force depend on the units used for mass, velocity, and radius. However, in the SI system, the unit for centripetal force is Newtons (N).

How do you calculate the speed of an object in circular motion?

The speed of an object in circular motion can be calculated using the formula v = 2πr/T, where v is the speed, r is the radius of the circle, and T is the time taken for one complete revolution. This formula assumes that the object is moving at a constant speed.

What factors affect the centripetal force on an object?

The centripetal force on an object is affected by the mass of the object, the speed at which it is moving, and the radius of the circular path. As these factors increase, the centripetal force also increases.

Can centripetal force be greater than the weight of an object?

Yes, centripetal force can be greater than the weight of an object. This is because centripetal force is dependent on the object's mass, speed, and radius, while weight is only dependent on the object's mass and gravity. Therefore, an object can experience a centripetal force greater than its weight and still remain in circular motion.

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