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tensions in the strings and accelerations of the object

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An object of mass m1 on a frictionless horizontal table is connected to an object of mass m2 through a very light pulley P1 and a light fixed pulley P2 as shown below.

(a) If a1 and a2 are the accelerations of m1 and m2, respectively, what is the relation between these accelerations?

(b) Express the tensions in the strings in terms of g and the masses m1 and m2.

(c) Express the accelerations a1 and a2 in terms of g and the masses m1 and m2.

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It finds the tensions in the strings and accelerations of the object in the two objects and two pulleys system. The solution is detailed and was rated '5/5' by the student who posted the questions.

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An object of mass m1 on a frictionless horizontal table is connected to an object of mass m2 through a very light pulley P1 and a light fixed pulley P2 as shown below.

(a) If a1 and a2 are the accelerations of m1 and m2, respectively, what is the relation between these accelerations?
Let x2 be the distance from the wall to moving pulley P1; clearly the position of m2 is also measured by x2. is the length of string from m1 to P1. x1 measures the distance ...

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