Centripetal Force Problem: Calculating Speed of a Model Airplane on a String"

AI Thread Summary
The discussion revolves around calculating the speed of an 82 g model airplane flying in a horizontal circular path with a string exerting a force of 3.22 N. The key equation used is centripetal force, represented as F(c) = mv²/r. Participants clarify that the weight of the airplane does not affect the horizontal force exerted by the string, emphasizing that only the force along the string is relevant for this calculation. The confusion arises from the initial approach of using vector components, which is unnecessary since the problem assumes an ideal horizontal scenario. Ultimately, the focus remains on applying the centripetal force formula directly to find the speed of the airplane.
Haniszmi
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Homework Statement


A person is flying an 82 g model airplane in a horizontal circular path on the end of
a string 11m long. The string is also horizontal (ideal situation). It exerts a force of
3.22N on the hand of the person holding it. What is the speed of the plane?




Homework Equations


Force(c)=mv^2/r


The Attempt at a Solution


I did the problem by using vector components. 3.22N was the force acting on the arm to the right and the other component was the force of gravity which was N=mg, 803.6N acting down. I used pyth. theorem to find the hypotenuse. Then i go to the solution manual to see if I did my work correctly so far and it turns out that they just substituted all the variables in the formula and got the answer without playing with any components. Why is this so? Please help!
 
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Haniszmi said:

Homework Statement


A person is flying an 82 g model airplane in a horizontal circular path on the end of
a string 11m long. The string is also horizontal (ideal situation). It exerts a force of
3.22N on the hand of the person holding it. What is the speed of the plane?

Homework Equations


Force(c)=mv^2/r

The Attempt at a Solution


I did the problem by using vector components. 3.22N was the force acting on the arm to the right and the other component was the force of gravity which was N=mg, 803.6N acting down. I used pyth. theorem to find the hypotenuse. Then i go to the solution manual to see if I did my work correctly so far and it turns out that they just substituted all the variables in the formula and got the answer without playing with any components. Why is this so? Please help!

The weight of the plane has nothing to do with the force on the hand. The force on the hand is coming from the string. The string is horizontal. So only the force along the string is what counts and that is mv2/R

Note also: The plane is given as grams not kg.
 
Haniszmi said:

Homework Statement


A person is flying an 82 g model airplane in a horizontal circular path on the end of
a string 11m long. The string is also horizontal (ideal situation). It exerts a force of
3.22N on the hand of the person holding it. What is the speed of the plane?




Homework Equations


Force(c)=mv^2/r


The Attempt at a Solution


I did the problem by using vector components. 3.22N was the force acting on the arm to the right and the other component was the force of gravity which was N=mg, 803.6N acting down. I used pyth. theorem to find the hypotenuse. Then i go to the solution manual to see if I did my work correctly so far and it turns out that they just substituted all the variables in the formula and got the answer without playing with any components. Why is this so? Please help!
The problem states that the string is horizontal and that the airplane path is in a horizontal circle (ideal situation). But as long as there is mass at the end of the string, it can never be truly horizontal, because the weight tof the mass will pull the string down a bit from the horizontal. The problem is asking you to ignore this effect.
 
Awesome thanks guys!
 
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