a 280 kg crate is supported by several rope and pulley arrangementsas shown. Det

Question

a 280 kg crate is supported by several rope and pulley arrangementsas shown. Determine for each arrangement the tension in therope.

I know what the answer is, i need help understanding how thatbecame the answer as slow as possible please.
This is my first engineering class and i want to understand everything perfectly.

I am having trouble understanding how you get 2T=mg
3T, 4T....etc

Explanation / Answer

The main thing you always need to do "First" is draw free bodydiagrams. For part a) you have a rope attached to the top and thenrunning through the pully and up. Imagine you are holding therope at the arrow pointing upward. +up Fy = 0 for equilibrium. So, T + T - W = 0 =>>   2T = W. For case b) you have a rope attached to the top then runningthrough a pully at the bottom and one more at the top with thearrow pointing down. In this case you take the arrow pointingdown as the same T as the rope to the left. So, again for this case you would have 2T = W. For c) you can see a pully at the top with one of the ropesattached to the pully at the bottom then running up and over thetop pully and back under the bottom one with an arrow pointingupward. Again, imagine you're holding this rope with thearrow pointing up. Fy = 0 again will yield 3T = W for d) you have an arrow pointing down as in case b), so itwill be the same as the rope on the other side of the upperpulley. Again for this case you will yield 3T = W from your equillibriumequations. For e) you have 3 ropes grouped and one end with an arrow pointingupward. As I showed in case a) and c), imagine you holdingthe end of that rope. So this time you can see the trend andyou will end up with : 4T = W from your equillibrium equations. Hope this helpedsome or enough. You just kinda have to develop a sense ofthis kind of problem. It will come.

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