# Centripetal Force of a tied ball

• Touchme
In summary, the conversation is about finding the angle x of a 0.50 kg ball that is tied to the end of a 1.0 m light cord and is being revolved in a horizontal plane with a 30° angle with the vertical. The question is how to solve for x using the equations T = mg / cos(x), Fc = Tsin(x) = (mg)[tan(x)], and r = 1sin(x). The conversation also includes finding the speed of the ball and the angle of the cord with the vertical if the speed is changed to 4.0 m/s.
Touchme
A 0.50 kg ball that is tied to the end of a 1.0 m light cord is revolved in a horizontal plane with the cord making a 30° angle, with the vertical (See Fig. P7.52.)

I managed to get my answer down to solving for theta however I don't know how to do the math:

I solved for T = mg / cos(x)
The Fc is = Tsin(x) = (mg)[tan(x)]
(mg)[tan(x)] = (mv^2) / r

The following equation is where I am stumped...
sin^2(x) / cos(x) = 8 / 4.9

#### Attachments

• p7-52.gif
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Are you trying to find the speed?

Calculate Fc from Tsin(x) = (mg)[tan(x)]

Then calculate r, and you can find v.

I don't understand why you're stumped at that point, since you know what x is.

sorry for not clarifying my question. I am trying to solve for x. The question is: If, instead, the ball is revolved so that its speed is 4.0 m/s, what angle does the cord make with the vertical?

OK - sorry for delay - site wouldn't let me post

sin^2(x) / cos(x) = 8 / 4.9

Gives you 4.9 sin^2 x = 8 cos^2 x

Remember sin^2 x = (1 - cos^2 x) - substitute this and you should be able to solve for cos x (might be a quadratic you have to solve)

thank you so much.

## What is centripetal force?

Centripetal force is the force that acts on an object moving in a circular path, directed towards the center of the circle.

## How is centripetal force related to a tied ball?

A tied ball experiences centripetal force because it is constrained to move in a circular path by the string or rope that it is tied to.

## What factors affect the centripetal force of a tied ball?

The centripetal force of a tied ball is affected by the mass of the ball, the speed at which it is moving, and the radius of the circular path it is following.

## How is the direction of centripetal force determined?

The direction of centripetal force is always towards the center of the circle, perpendicular to the velocity of the object at any point on the circular path.

## Can centripetal force be calculated?

Yes, centripetal force can be calculated using the equation F = mv^2/r, where F is the force, m is the mass of the object, v is its velocity, and r is the radius of the circular path.

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