physics question

[pizza1994]

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A 1kg ball is swung around in a 90 cm circle at an angle of 10 degrees below the horizontal. What is the tension in the string?

Hi all is anyone getting mg/cos10 for this? This is what I'm getting but I'm not sure... 🙁

 

[pizza1994]

Im thrown off by the "below the horizontal" part....

 

[JMMTB]

Imagine the ball is swung around a pole, like a tetherball. If we draw a line parallel to the ground at the point where the string is attached to the pole this is "the horizontal." This line is perpendicular to the pole and we then have 10 degrees between this imaginary line and the string and then 80 degrees between the string and the pole.

Also remember there are 3 forces acting on the ball.

Good luck.

 

[Skizye]

Imagine the ball is swung around a pole, like a tetherball. If we draw a line parallel to the ground at the point where the string is attached to the pole this is "the horizontal." This line is perpendicular to the pole and we then have 10 degrees between this imaginary line and the string and then 80 degrees between the string and the pole.

Also remember there are 3 forces acting on the ball.

Good luck.

Isn't it just gravity and tension acting on the ball? What is the 3rd force?

 

[DrknoSDN]

Isn't it just gravity and tension acting on the ball? What is the 3rd force?

I thought that when i read it but didn't say anything. There are just 2 forces in that scenario.

 

[el_duderino]

The third force is centrifugal, from the perspective of the ball.

Draw the ball and rope. Draw the force due to gravity, 1kg * 9.8 m/s^2 = 9.8N

Draw the veritcal and horizontal component of the force from the rope. The vertical component will be equal to the force of gravity, or 9.8 N. The horizontal part will be equal and opposite to the centrifugal force, which you don't care about.

So you have a triangle with 9.8 on one side, a 10 degree opposite angle, and a hypotenuse of t. t is the tension.

 

[DrknoSDN]

That has come up in other threads. I'm not sure you can consider centrifugal force a real force here. The system your trying to draw is what forces are acting on the ball. Not the force of the ball on itself.

The only forces on the ball are gravity and tension. The vertical component of tension is sufficient to counter gravity. The horizontal component of the same tension force provides the "centripetal" acceleration. Similar to a normal force only being one force despite having vertical and horizontal components in some scenarios.

 

[JMMTB]

Shoot ya. Didn't think that one through all the way, sorry about that.

 

[el_duderino]

It doesn't really matter if you consider centrifugal force real or not. It's of course not real, but it makes the FBD a little more straighforward because all the forces balance out. Of course, the weight is accelerating so they don't actually balance out, but they do from the weight's non-inertial reference frame.

But it doesn't matter, since the only action you care about is in the vertical plane. The vertical component of the tension must cancel out gravity, and we have a 10 degree angle. That's all that's important.