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 = 1.90 kg, m2 = 2.90 kg, and m3 = 4.85 kg. (a) Find the tension T in 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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