Anobject of mass m, hangs fromstring that passes over a very light faed putey Pi

Question

Anobject of mass m, hangs fromstring that passes over a very light faed putey Pi as shown in the fore below. The string connees to a second wry this pulley with one end attached to a wall and the other to an object of mass m on a frictioniless, horizontal tabie. puley P2. Asecond tring pense am (a) fai "d a2 are the accelerations of mi rd ma, respectively, weat is the relation between these accelerations? (use any variable or symbol stated above as necessary.) (b) Find expressions for the tensions in the strings in terms of the masses m and m and g (c) find expressions for the accelerations a1 and a in terms of the masses m and ma, and g

Explanation / Answer

a] a2 = 2a1

b] m1g - T1 = m1a1

T2 = m2a2

also, T2 = 0.5T1

T1 = 2T2 = 2 m2a2

Adding it to the first equation, m1g = m1a1 + 2m2a2 = m1a1 + 4m2a1

a1 = m1g/[m1+4m2]

a2= 2*m1g/[m1+4m2]

T2 = 2m2 m1g/[m1+4m2]

T1 = 4m2 m1g/[m1+4m2] and T2 = 2m2 m1g/[m1+4m2]

c] From above part

a1 = m1g/[m1+4m2]

a2= 2*m1g/[m1+4m2]

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