In the figure, three boxes are connected by cords, one of which wraps over a pul

Question

In the figure, three boxes are connected by cords, one of which wraps over a pulley having negligible friction on its axle and negligible mass. The three masses are md-30 kg, mB = 10 kg, and mc= 40 kg. when the system is released from rest, mass md 1s accelerated to the right, while mB and mc are accelerated downward. The coefficient of kinetic friction between mass ma and the horizontal surface is 0.2 a. What is the frictional force on m as it slides to the right? b. What is the net external force on the three-box system? c. What is the acceleration of mass mA? d. What is the tension in the cord that connects mass ma to mB?

Explanation / Answer

a.

fk = frictional force on A = uk mA g = (0.2) (30) (9.8) = 58.8 N

b)

Fnet = fk = frictional force = 58.8 N

c)

for combination of hanging block B and C

(mB + mC) g - T = (mB + mC) a

T = (mB + mC) g -  (mB + mC) a eq-1

T - fk = mA a

using eq-1

(mB + mC) g -  (mB + mC) a - fk = mA a

a = ((mB + mC) g - fk )/(mA + mB + mC)

a = ((50) (9.8) - 58.8)/(50 + 30) = 5.4 m/s2

d)

T = (mB + mC) g -  (mB + mC) a

T = (50) (9.8) - (50) (5.4)

T = 220 N

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