# Circular Motion Problem

1. Apr 23, 2004

### st3dent

A model plane of mass .75 kg is flying at a constant speed in a horizontal circle connected to a 30 m cord and is at a height of 18 m. The other end of the cord is tethered to the ground as shown in the picture. The plane makes 4.4 revolutions per minute, and the force that the air exerts on the plane is perpendicular to the wings. What is the tension in the cord?

I can see that the ball moves in constant circular motion with r as its radius.

I know that since the ball makes 4.4 revolutions/minute means that the ball has a period(T) of 13.63 seconds.

I also realize that the sum of all forces = ma
As F = ma, Gm1m2/ r2 = ((m)(4 pi2)(r)) / T2

I see that the force of tension (Ft) has an upwards component of Ftsinx that balances the downwards mg and a left component of Ftcosx that directly causes the circular motion.

However, I do not know how to approach this problem.
Where do I start...your help is much appreciated.

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Last edited: Apr 23, 2004
2. Apr 24, 2004

### swansont

Any object moving in a circle at constant speed must feel a force of mv2/r toward the center. In this case, what could be supplying that force?

3. Apr 25, 2004

### st3dent

Gravity....but how do I solve this damn problem?

4. Apr 25, 2004

### Staff: Mentor

Use Newton's 2nd law! First identify all the forces on the plane. Then realize that the acceleration is centripetal, as swansont explained. Hint: the air pushes up (and back) on the plane, gravity pulls down... what is pulling it toward the center?

5. Apr 25, 2004

### HallsofIvy

Staff Emeritus
NO! Gravity pulls downward. The plane is not going downward, it is going in a horizontal circle. What is keeping the plane in that circle?