An object of mass m1 hangs from a string that passes over a very light fixed pul

Question

An object of mass m1 hangs from a string that passes over a very light fixed pulley P1 as shown in the figure below. The string connects to a second very light pulley P2. A second string passes around this pulley with one end attached to a wall and the other to an object of mass m2 on a frictionless, horizontal table. (a) If a1 and a2 are the accelerations of m1 and m2, respectively what is the relation between these accelerations? (Use any variable or symbol stated above as necessary.) a2= X (b) Find expressions for the tensions in the strings in terms of the masses m1 and m2 and g. (c) Find expressions for the accelerations a1 and C2 in terms of the masses m1 and m2 and g.

Explanation / Answer

a)

a1 =2a2

b) let T2 =T

then T1 =2T

let a1= a

a2 =2a

m1g-T1= m1a1 this be eqaution 1

T2 = m2a2

m1g-2T = m1a

T = 2m2a

m1g - 4m2a = m1a

a = m1g/(m1+4m2)

T = 2m2m1g/(m1+4m2)

therefore

T1 = 4 *m2m1g/(m1+4m2)

T2 =  2*m2m1g/(m1+4m2)

a1 = m1g/(m1+4m2)

a2 = 2*m1g/(m1+4m2)

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