Difference between applied tension and tension due to weight?

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SUMMARY

The discussion clarifies the difference between applied tension and tension due to weight in a physics problem involving a block on a table and a hanging mass. In Case I, a direct applied tension of 50 N results in a tension of 50 N. In Case II, with a 5 kg block and a 10 kg block on the table, the tension is calculated to be 40 N due to the effects of acceleration and friction. The equation mg - Fs = (M+m)a is used to derive the acceleration and subsequently the tension in the system.

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Petrikovski
im trying to do this AP problem that involves a block on a table attached to a string which hangs over a pulley. in Case I 50 N is applied to the string and in Case II a 5 kg block is attached. the tension in Case I is 50, but according to my packet in case II the tension in Case II is 40. why would 50 N applied directly be more tension than Fw = 5x10 = 50 N?
 
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btw the block on top is 10kg and there is a coefficient of friction of .2
 
Because in the second case there is more mass so there's less acceleration:
mg - Fs = (M+m)a
50 - 20 = 15a
a = 2
Now looking at the 5kg weight:
50 - T = 5a
T = 50 - 10 = 40
 

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