Circular Motion/Centripetal Forces

In summary, the problem involves a 2.1 kg mass attached to a .5m string that is whirled in a horizontal circular path. The maximum tension the string can withstand is 80N. Using the equation Ac = v^2/r, the maximum speed of the mass is calculated to be 4.36 m/s. If the system were not horizontal, the force of gravity would need to be factored in as well.
  • #1
omgitsmonica
22
0

Homework Statement


A 2.1 kg mass is attached to the end of a .5m string. The system is whirled in a horizontal circular path. If the maximum tension that the string can withstand is 80N, what is the maximum speed in m/s of the mass if the string is not to break?


Homework Equations



Ac=v2/r


The Attempt at a Solution


I have no idea how to go about solving this. I don't know what mass has to do with anything...
 
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  • #2
You have the right equation for a, just put it into Newton's second law.
 
  • #3
F=ma, so 80N=2.1a so 38.1=a

Ac=v2/r, so 38.1=v^2/.5

So v^2=19.05, so v = 4.36

Is that right?
 
  • #4
Yes

So the Fnet is the Ft and it is equal to mv^/r

But the key word in this questions is its horizantal. Do you know what would be diffirent if it wasnt horizantal?
 
  • #5
I imagine it would be the acceleration, because the direction of motion would be changed. Or does that not matter, like trajectories?
 
  • #6
If it is horizantal the only thing would be different is that gravity acting on the object that is spinning should also be factored in into the Fnet formula.

So at the top

Fc= Ft + Fg

Bottom

Fc= Ft-Fg
 

1. What is circular motion?

Circular motion is the movement of an object along a circular path. This type of motion is characterized by a constant speed, but a changing direction. An example of circular motion is a car traveling around a roundabout.

2. What is a centripetal force?

A centripetal force is a force that acts towards the center of a circular path, keeping an object moving in a circular motion. It is necessary to maintain the object's circular motion and prevent it from flying off in a straight line.

3. How is centripetal force related to circular motion?

Centripetal force is directly related to circular motion because it is the force that keeps an object moving in a circular path. Without a centripetal force, an object would continue in a straight line tangent to the circle.

4. What are some examples of centripetal forces?

Examples of centripetal forces include gravity, tension in a string or rope, and friction. For instance, gravity acts as a centripetal force when keeping the planets in orbit around the sun, and tension in a string is a centripetal force when swinging a bucket of water around in a circle.

5. How is centripetal force calculated?

The formula for calculating centripetal force is Fc = mv²/r, where Fc is the centripetal force, m is the mass of the object, v is its velocity, and r is the radius of the circular path. This formula shows that centripetal force is directly proportional to the mass and velocity of the object and inversely proportional to the radius of the circle.

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