Posted by **Steven** on Wednesday, December 8, 2010 at 1:37pm.

Ball, with a weight of 200 grams, tied to a string rotates around in a horizontal plane. Period of rotation is 2 seconds. What is the force (in N) which acts on the string? The length of the string is 0.5 meters.

- Physics -
**MathMate**, Wednesday, December 8, 2010 at 1:58pm
The force on the string is composed of two components, the weight of the ball, fy=mg, and the centripetal force due to rotation, fx=mrω².

m=0.2 kg

r=0.5m

ω=2π/2s=π rad./s

Resultant force

=√(fx²+fy²)

- Physics -
**drwls**, Wednesday, December 8, 2010 at 2:37pm
I have a different interpretation of this problem. r is the radius of the circular path of what is in this case a conical pendulum, not the length of the string.

Let the string tension be T. Let the string angle from vertical be A. Let the period be P = 2s

T cos A = M g

T sin A = M V^2/R

= M*(2 pi)^2 R/P^2

T^2 = M^2 [g^2 + (2 pi)^4*(R^2/P^4)]

You can also solve for the angle A,

tan A= (2*pi)^2*R/(P^2/g)

which leads to

P = 2 pi sqrt[R/(g tanA)]

= 2 pi sqrt[R cosA/sinA]

= 2 pi sqrt(L cosA/g)

For an L = 0.5 m length string, with a period of P = 2s

L cosA/g = 1/pi^2 s^2

This leads to an impossible value for cos A, greater than 1

The problem is overdetermined and the input data are inconsistent. The period of a mass on a string 0.5 m long in a conical orbit cannot be as long as 2 seconds. The same applies to a plane pendulum of that length.

- Physics -
**MathMate**, Wednesday, December 8, 2010 at 3:20pm
I agree that it is impossible.

My previous solution omitted the reduction of radius as the angular speed is decreased.

If L=length of the string,

and θ=angle of string with vertical,

then

tan(θ)=fx/fy

=m(l*sin(θ)ω²/mg

On simplicication,

cos(θ)=g/(Lω²)

=9.81/(0.5*π²)

=1.98 which is impossible

For the system to work, either the length has to be doubled, or the period reduced to 1.4 sec. or less

In short, the data from the question should be confirmed or revised.

## Answer this Question

## Related Questions

- Physics - You plan to fly a model airplane of mass 0.655 kg that is attached to ...
- Physics - You plan to fly a model airplane of mass 0.655 kg that is attached to ...
- Physics Help - A ball of mass 1.76 kg is tied to a string of length 4.19 m as ...
- PHYSICS!! - A ball on the end of a string is whirled around in a horizontal ...
- AP Physics - A girl is whirling a ball on a string around her head in a ...
- physics - a framed picture of weight 15N is hung on a wall, using a piece of ...
- Physics - A ball on the end of a string is whirled around in a horizontal circle...
- Physics - A 3.1 kg ball is tied to a string and swung in a horizontal circle at ...
- PHYSICS - A 0.4 kg toy tied on a string can be whirled in a horizontal circle of...
- physics - a ball of weight 200 grams,is tied to the end of a cord and whirled in...

More Related Questions