Three objects are connected on the table as shown below. The coefficient of kine

Question

Three objects are connected on the table as shown below. The coefficient of kinetic friction between the block of mass m2 and the table is 0.475. The objects have masses of m1 = 4.30 kg, m2 = 1.50 kg, and m3 = 2.25 kg, as shown, and the pulleys are frictionless. A. Determine the acceleration of the 4.30 kg object, including its direction. B. Determine the acceleration of the 2.25 kg object, including its direction. C. Determine the acceleration of the 1.50 kg object, including its direction. D. Determine the tensions in the two cords.

Explanation / Answer

net horizontal force on the mass m2 by the weights of other two masses = (4.3-2.25)*9.81=20.11 N

normal upward force on mass m2 , N = 1.5*9.81 = 14.71 N

so maximum frictional force Fmax = 0.475*14.71 =6.99 N

we can see that horizontal force by masses is greater than maximum frictional force so mass will move

by force Fnet = 20.11-6.99 = 13.12 N towards left

and as string is same all the system has same acceleration

and their acceleration , a = 13.12/1.5 = 8.75 m/s2

(A) acceleration of 4.30 kg object = a = 8.75 m/s2 downwards

(B) acceleration of 2.25 kg object = a = 8.75 m/s2 upwnwards

(C) acceleration of 1.50 kg object = a = 8.75 m/s2 towards left

(D) since pulley is frictionless

tension in the chord with mass m3 = 2.25*9.81 = 22.07 N

tension in the chord with mass m1 = 4.30*9.81 = 42.18 N

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