Tension Vectors - Grade 12 Algeo

[lalota]

Please help, I cannot figure this problem out and I would appreciate any assistance. Sorry if this seems ridiculously easy to some of you. I have an idea of what might happen, but I'm really not sure at all. The problem is in the following image:

http://img15.exs.cx/img15/9651/mathhelp.jpg

Any help at all! Thanks so much!

 

[NateTG]

Well, each weight can go up, down, or stay in place. Since there are only 3 weights, that makes for 27 possible circumstances. You could work through all of them, to see which one makes sense. You might figure out some stuff after checking a couple of possibilities.

 

[lalota]

Thank you for the hint! I have a feeling that since the tension is greater in the shorter line supporting the 4kg mass, it might affect the final outcome. Am I on the right path?

 

[NateTG]

My apologies. I think I misunderstood the problem a bit.

Thank you for the hint! I have a feeling that since the tension is greater in the shorter line supporting the 4kg mass, it might affect the final outcome. Am I on the right path?

It's not actually clear from the illustration whether the connection between the string holding the 4kg weight and the other string is free-moving, but I would guess it is not because there is no pulley, so you should probably think of it as three strings coing into the junction instead of 2, and then the 5kg string would have more tension in it.

You also know that the string on the 4kg weight is always going to pull straight down.

The trick is to set up angles at the meeting of the three strings so that the total tension adds up to zero.

 

[lalota]

Sorry, there's something I don't quite grasp. Why would the 4kg mass always pull straight down? Wouldn't the 5kg mass keep it from doing so because it too would try to pull straight down?

I definitely see what you mean about the angles, and I'll try working with that now. Since it wants to reach an equilibrium, all the forces/tension must cancel out to zero.

Are there any other points I should know besides this? This question is part of the dot product/cross product unit... so would those come into play at all?

 

[lalota]

Sorry again... this is very urgent, as I have to know this question for a test tommorow. Any further help is truly appreciated!

 

[NateTG]

Sorry, there's something I don't quite grasp. Why would the 4kg mass always pull straight down? Wouldn't the 5kg mass keep it from doing so because it too would try to pull straight down?

I definitely see what you mean about the angles, and I'll try working with that now. Since it wants to reach an equilibrium, all the forces/tension must cancel out to zero.

Are there any other points I should know besides this? This question is part of the dot product/cross product unit... so would those come into play at all?

This is probably too late for help on the test, but I was thinking of the tensions where the three strings meet. The string that the 4kg weight is on is not being redirected by any pulleys there, so it must be pulling down. The other two are redirected by pulleys, so they can pull in different directions (if that makes any sense.)

I would be inclined to solve the problem using component-wise operations. I don't think that dot or cross products are natural expressions for resolving this problem.

 

[lalota]

Thanks Nate! Yep, too late for the test, but I was able to figure out what you orginally meant. I created a triangle using the forces of each mass that would illustrate how the forces cancel to create an equilibrium. We weren't required to find the angles, but tried to show that the main system (4 kg going down, 3 kg up left, 5 kg up right) would create an equal resulatant in the opposite direction of the 4 kg mass. Hopefully that was right!... if it wasn't, then "oh well". :P

 

[NateTG]

Sounds like you're on top of things. Hope you did well.