Two boxes of fruit on a frictionless horizontal surface are connected by a light

Question

Two boxes of fruit on a frictionless horizontal surface are connected by a light string as in the figure below, where m1 = 11 kg and m2 = 22 kg. A force of 80 N is applied to the 22 kg block.

(a) Determine the acceleration of each block and the tension in the string.
acceleration of m1_____m/s2
acceleration of m2_____m/s2
tension in the string____N

(b) Repeat the problem for the case where the coefficient of kinetic friction between each block and the surface is 0.10.
acceleration of m1____m/s2
acceleration of m2____m/s2
tension in the string____N

Explanation / Answer

the masses m1 = 11 kg , m2 = 22 kg      force F = 80 N (a)        According to Newton's second law of motion, F = (m1+m2)a    a = 80/33    a = 2.42 m/s^2 acceleration of m1 is 2.42 m/s^2 acceleration of m2 is 2.42 m/s^2 the tension in the string , T = m1a = 11*2.42 = 26.66 N (b) if the friction is acting on the surface, = 0.10      Applying the Newton 2nd law of motion,    F = F-f1-f2 where f1 = m1g =0.10*11*9.8 = 10.78 N f2 = 0.10*22*9.8 = 21.56 N therefore    F = 80 - 32.34                          = 47.66 the acceleration , a = F/(m1+m2) = 1.44 m/s^2 acceleration of m1 is 1.44 m/s2 acceleration of m2 is 1.44 m/s2 the tension, T = m1a + f1                  T = 15.88 + 10.78                  T = 26.66 N

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