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

[Haniszmi]

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!

 

[LowlyPion]

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.

 

[PhanthomJay]

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.

 

[Haniszmi]

Awesome thanks guys!