What is the solution to the Kinematics of Particles Homework?

AI Thread Summary
The discussion focuses on solving a kinematics problem involving forces acting on a ball before and after a string is cut. The initial approach involved summing forces in the y-direction, leading to an expression for tension in terms of the ball's weight. Participants pointed out the need for clarity in calculations and the correct use of trigonometric functions, specifically questioning the use of cos40° after the string is cut. The correct interpretation of the y-axis orientation and the gravitational force components was emphasized, particularly how to express the weight in terms of mg sin40°. The conversation concludes with a confirmation that understanding the angle's impact on the calculations is crucial for arriving at the correct solution.
Auburn2017
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Homework Statement


Refer to figure please.

Homework Equations


∑Fy=0 before string is cut

The Attempt at a Solution


I tried summing the two forces in the y direction before the strings were cut which would be the two tensions at a sin40° and minus the weight of the ball(mg). That gave me T in terms of mg. Then I summed the forces when the string was cut and got T minus mgcos40. Then I thought that would be my ratio but my answer didnt match that of the solution. Help Please!
 

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Your approach seems good. Are you sure that you should be using cos40o in the calculation after the string is cut? You left out the details of your calculations and you did not state what you actually got for the tension before and after one of the strings is cut.
 
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TSny said:
Your approach seems good. Are you sure that you should be using cos40o in the calculation after the string is cut? You left out the details of your calculations and you did not state what you actually got for the tension before and after one of the strings is cut.
This is what I ended up doing. Does my work look right or did I just happen to get it right? Oh and there should be a mg on the end of my T=0.643 equation. I don't really know why I used mgsinΘ, I just know it gets you the right answer. An explanation on that would be greatly appreciated.
 

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In your first diagram your analysis looks good. Here you are taking the y-axis to be vertically upward.

In your second diagram (one string), what direction are you taking for the y-axis? Also, you should show the gravitational force in this diagram.
 
TSny said:
In your first diagram your analysis looks good. Here you are taking the y-axis to be vertically upward.

In your second diagram (one string), what direction are you taking for the y-axis? Also, you should show the gravitational force in this diagram.
Oh that is what it is. If you take the y-axis to be at an angle of 40 degrees then the y component of the weight becomes mg sin40. Makes sense now.
 
OK. Good work.
 
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Thread 'Collision of a bullet on a rod-string system: query'

Thread 'Collision of a bullet on a rod-string system: query'

In this question, I have a question. I am NOT trying to solve it, but it is just a conceptual question. Consider the point on the rod, which connects the string and the rod. My question: just before and after the collision, is ANGULAR momentum CONSERVED about this point? Lets call the point which connects the string and rod as P. Why am I asking this? : it is clear from the scenario that the point of concern, which connects the string and the rod, moves in a circular path due to the string...
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