I Understanding tension and centripedal force in a puck and weight

AI Thread Summary
The discussion centers on understanding the mechanics of tension and centripetal force in a system involving a puck and a weight. The net force equations reveal that tension is crucial for maintaining the puck's circular motion, as it provides the necessary centripetal acceleration. The tension in the rope acts inward on the puck while simultaneously exerting an upward force on the weight, creating a complex interaction. The participants clarify that tension in a rope does not have a single directional force but acts in both directions at once, affecting both the puck and the weight. This exploration reinforces the importance of accurately visualizing force interactions in physics problems.
ago01
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For practice I did the following problem:

1646538635747.png


Solving this problem mechanically was simple enough using the following force diagrams:

1646539166892.png
Then

$$F_{net_M} = T - Mg = 0$$

Due to the stationary condition

$$T = mg$$

and

$$F_{net_m} = T = ma_c$$

$$T = ma_c$$

Because centripedal acceleration is inward the direction of the tension. The rope is pulling on the puck to stay in the circle, because without it the puck would simply fly away.

So we find after substitution:

$$Mg = m\frac{v^2}{R}$$

and after some algebra

$$v = 1.8 \frac{m}{s}$$.So algebraically this problem wasn't terrible. Understanding the nature of the forces wasn't too bad either...at least mechanically. However I'm left wondering how exactly this tension is behaving.

Since the the rope is pulling inward on the puck it is imposing some centripedal force on the puck, and this force is causing the centripedal acceleration experienced (and what is holding the puck on the radius).

However, the rope is also pulling up on the weight. So the tension in the rope is inward facing (towards the hanging weight), yet the weight experiences some upward tension to balance out gravitational force as well! My intuition is failing me.

Is this because of the right angle it is creating? The tension is inward on the table, but upward on the weight opposite gravity. Does this have something to do with the angle it's creating? If gravity and centripedal acceleration are both inward (gravity being "down and in") I would expect the rope to be slack. I'm trying to quantify this but I am failing at coming up with a way to explain it. Which bothers me because I've seen the experiment done before.
 
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ago01 said:
So the tension in the rope is inward facing
Can you clarify what you mean when you say that tension in a rope has a direction toward one end and away from the other?

Hint: It does not.
 
jbriggs444 said:
Can you clarify what you mean when you say that tension in a rope has a direction toward one end and away from the other?

Hint: It does not.

Sure, I'll diagram what's going on in my brain

1646541222941.png


This was my original post diagrammed. However, it appears I forgot a very important condition...

1646541496166.png


I'm not sure if this is totally correct...but it feels closer. So because the puck is spinning a circle, the changing velocity is generating a centripedal acceleration. This centripedal acceleration is the inward tension. But, the puck is also "pulling back" on the weight by being held along the radius by this acceleration.
 
Right. The tension in the cord works both ways.

It pulls left on the corner of the hole in the table. It pulls right on the puck.
It pulls down on the corner of the hole in the table. It pulls up on the weight.
 
jbriggs444 said:
Right. The tension in the cord works both ways.

It pulls left on the corner of the hole in the table. It pulls right on the puck.
It pulls down on the corner of the hole in the table. It pulls up on the weight.

I see yep. I'm glad I asked. This is a good checkpoint for me on making sure I'm getting force pairs correctly.

Thank you!
 
Hello everyone, Consider the problem in which a car is told to travel at 30 km/h for L kilometers and then at 60 km/h for another L kilometers. Next, you are asked to determine the average speed. My question is: although we know that the average speed in this case is the harmonic mean of the two speeds, is it also possible to state that the average speed over this 2L-kilometer stretch can be obtained as a weighted average of the two speeds? Best regards, DaTario
This has been discussed many times on PF, and will likely come up again, so the video might come handy. Previous threads: https://www.physicsforums.com/threads/is-a-treadmill-incline-just-a-marketing-gimmick.937725/ https://www.physicsforums.com/threads/work-done-running-on-an-inclined-treadmill.927825/ https://www.physicsforums.com/threads/how-do-we-calculate-the-energy-we-used-to-do-something.1052162/
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