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I guess it depends on how you started out the problem.
If you treated the cart and drum as a single system, the reaction at O (force of cart on drum or the force of drum on cart) does not appear since it is an internal pair of forces that cancel. With this approach, you cannot find the reaction at O.
If you treated the cart and drum as individual systems, the reaction at O is exposed, both the force of drum on cart and force of cart on drum. This method will allow you to calculate the reaction at O.
Having said all of that, please keep in mind that whether or not you are able to actually calculate a reaction does not dictate whether or not it has an influence on the motion. That is, both methods (two systems or one single system) above will give the same answer regardless of whether you are able to calculate the reaction at O.
My thoughts were that when I plugged values into the linear impulse momentum equation, it wouldn't be T that I was plugging in as the net force. It seems like you 'lose' something because that force is also changing the angular momentum of the drum. For example, if T was acting right on the cart, the cart would have greater momentum change than the case shown in this problem. My question is really which forces are responsible for changing the momentum of the cart?
Thanks for clarifying your question. I now better understand your point.
Take a look at the sketch of solution added to your original post (my HTML skills are not good enough to figure out how to put a link on a Comment...). You will see that putting T on the carriage has the SAME influence on the change in linear momentum of the system as having T applied to the drum. The difference between those two situation is on the angular momentum of the drum.
At first, this result of no change in linear momentum when the location of the application of T is changed might seem counterintuitive. However, in looking at the solution, it makes sense since T is solely responsible for changing linear momentum for the total system regardless of where it is applied. You cannot change the linear momentum of the drum without changing the linear momentum of the carriage.
I need to move my original description of your question as "good" up to "great" -- you have made a great point with your question!
4 comments:
And by momentum...I meant linear momentum.
I guess it depends on how you started out the problem.
If you treated the cart and drum as a single system, the reaction at O (force of cart on drum or the force of drum on cart) does not appear since it is an internal pair of forces that cancel. With this approach, you cannot find the reaction at O.
If you treated the cart and drum as individual systems, the reaction at O is exposed, both the force of drum on cart and force of cart on drum. This method will allow you to calculate the reaction at O.
Having said all of that, please keep in mind that whether or not you are able to actually calculate a reaction does not dictate whether or not it has an influence on the motion. That is, both methods (two systems or one single system) above will give the same answer regardless of whether you are able to calculate the reaction at O.
Good question.
Let us know if that does not help.
My thoughts were that when I plugged values into the linear impulse momentum equation, it wouldn't be T that I was plugging in as the net force. It seems like you 'lose' something because that force is also changing the angular momentum of the drum. For example, if T was acting right on the cart, the cart would have greater momentum change than the case shown in this problem. My question is really which forces are responsible for changing the momentum of the cart?
Thanks for clarifying your question. I now better understand your point.
Take a look at the sketch of solution added to your original post (my HTML skills are not good enough to figure out how to put a link on a Comment...). You will see that putting T on the carriage has the SAME influence on the change in linear momentum of the system as having T applied to the drum. The difference between those two situation is on the angular momentum of the drum.
At first, this result of no change in linear momentum when the location of the application of T is changed might seem counterintuitive. However, in looking at the solution, it makes sense since T is solely responsible for changing linear momentum for the total system regardless of where it is applied. You cannot change the linear momentum of the drum without changing the linear momentum of the carriage.
I need to move my original description of your question as "good" up to "great" -- you have made a great point with your question!
Let me know if this does not help.
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