Two blocks connected by a string are on a horizontal frictionless surface. The b

Question

Two blocks connected by a string are on a horizontal frictionless surface. The blocks are connected to a hanging weight by means of a string that passes over a pulley as shown in the figure below, where m1 = 2.20 kg, m2 = 2.85 kg, and m3 = 4.90 kg.

(a) Find the tensionTin the string connecting the two blocks on the horizontal surface.

(b) How much time is required for the hanging weight to fall 10.0 cm if it starts from rest?

Explanation / Answer

the forces acting on the hanging block are its weight and the tension of the first string up, so for that block we have T1 - m3 g = - m3 a the forces on m2 are T1 to the right and T2 to the left, or: T1 - T2 = m2 a for m1, the only force is T2 to the right, so we have T2 = m1 a sub for T2 in the second equation: T1-T2=m2 a -> T1- m1 a = m2 a or T1=(m1+m2)a substitute this into the m3 equation: (m1+m2)a - m3 g = -m3 a => (m1+m2+m3)a = m3 g a=m3 g/(m1+m2+m3) = 5.12m/s/s use dist = 1/2 at^2 or t=sqrt[2d/a] = sqrt[2*0.1m/5.12m/s/s] knowing a, substitute a into the T1 and T2 eqs to find T1 and T2

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