Circular motion involving friction and tension

In summary, the problem involves a block on a turntable attached to the center with a string of length 0.4m. The maximum tension the string can support is 300N, and the static friction constant between the table and the block is 0.8. Using equations for centripetal force and friction, the question asks how fast the table can spin without the string snapping. However, the mass of the block is not given, making it impossible to find a quantitative value for velocity.
  • #1
fighter2_40
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Homework Statement


There is a block on a turntable. It is attached to the center of the table by a string with the length .4m. Also the static friction constant between the table and the block is 0.8 .
If the maximum tension the string can support is 300n how fast can the table spin without the string snapping?

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Homework Equations


mass (velocity)^2 / radius = Centripetal Force
mass x 9.8 [gravity] x U [friction constant] = Force of Friction


The Attempt at a Solution



mv^2/.4 = 300 + .8mg

V = sqr(120/m +3.136)

Where do I go from here? Can I find a quantitative value for velocity if the mass of the block is not given?

Thanks! I would appreciate it if I can get an answer tonight. My impression is that this is due tomorrow.
 
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  • #2
The block is accelerating towards the center of the turntable. So the frictional force on the turntable is away from the center. Reaction to this frictional force on the block is towards the center.
Now rewrite the equation.
 
  • #3
rl, I'm not sure I follow. I understand that the block is accelerating towards the center. Aren't i only concerned with the friction force on the block, which is towards the center (this is part of the forces necessary for allowing the block not to move to a farther orbit).

What I don't understand is why my equation mv^2/r = Ftension + Ffriction towards the center is incorrect. Further I don't know how to solve this without a given mass. Perhaps my teacher had forgotten to give the mass.
 
  • #4
You are right. Mass must be given to solve the problem.
 

Related to Circular motion involving friction and tension

What is circular motion?

Circular motion is the movement of an object along a circular path. It involves a continuous change in direction, velocity, and acceleration.

What is friction in circular motion?

Friction is the force that opposes the motion of an object. In circular motion, friction acts tangentially to the motion and can either speed up or slow down the object depending on its direction.

How does tension affect circular motion?

Tension is a force that is transmitted through a stretched string or rope. In circular motion, tension is responsible for keeping the object moving in a circular path by constantly pulling it towards the center.

What factors affect the amount of friction and tension in circular motion?

The amount of friction and tension in circular motion can be affected by the mass of the object, the speed at which it is moving, and the surface it is moving on. For example, a heavier object will experience more friction and require more tension to maintain circular motion.

How can friction and tension be calculated in circular motion?

Friction and tension can be calculated using Newton's second law of motion, which states that the sum of all forces acting on an object is equal to its mass multiplied by its acceleration. By calculating the acceleration of the object in circular motion, the friction and tension forces can be determined.

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