A 5.00 kg object placed on a frictionless, horizontal table is connected to a string that passes over a pulley and then is fasted to a hanging 9.00 kg object. Find the acceleration of the two objects and the tension in the string.
First, there is just one force acting on the 5kg block, and it is the tension to the right (positive x axis; so Tension is positive). There is no acceleration in the y direction for the 5kg block:
F(y): n-mg = 0 or n=mg
For the 9kg block, there is T in the y direction and the force mg.
T-mg = ma(y)
T = ma + mg
Can someone help me?
Because of the pulley, the rightward acceleration "a" of the 5 kg object equals the downward acceleration of the 9 kg hanging mass. You can treat "a" as a single unknown and forget about the vector directions.
Let acceleration be positive to the right for the 5 kg mass and positive downward for the 9 kg mass. The rope tension is T on both objects for a frictionless massless pulley.
T = 5.0 a
9.0 g - T = 9.0 a
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9.0 g = 14.0 a
a = (9/14) g
T = 5 a = (45/14)g = 31.5 N
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