Two objects of unequal mass ml m 2.00 kg and m2 = 4.00 kg arc hung vertically ov

Question

Two objects of unequal mass ml m 2.00 kg and m2 = 4.00 kg arc hung vertically over a frictionless pulley of negligible mass, as shown in Figure. Determine the magnitude of the acceleration of the two objects and the tension in the lightweight cord. A block of mass ml= 6kg on a rough, horizontal surface is connected to a ball of mass m2=15kg by a lightweight cord over a lightweight, friction less pulley. as shown. A force of magnitude coefficient of kinetic friction between the block and surface is mu_k = 0.36 Determine the magnitude of the acceleration of the two objects.

Explanation / Answer

3. m1 = 2 kg

m2 = 4 kg

Frictionless and massless pulley .

Acceleration = a = {(m2 - m1)/(m1 + m2) }×g = g/3. = 9.8/3 = 3.27. m/s2

Tension in the sstring = T = m2×g - m2×a. = 39.2 - 13.08 = 26.12 N

4. Force F = 70 N

m1 = 6 kg , m2 = 1.5 kg

Equation of motion for m1

F ×Cos(60) - T - 0.36{ m1×g - F ×Sin(60) ) = m1×a

EEquation of motion for m2

T - m2 ×g = m2×a

On ssolving both equation we get

a = 2.64 m/s2

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