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 = 12 kg and m2 = 24 kg. A force of F = 56 N is applied to the 24-kg block.

(a) Determine the acceleration of each block and the tension in the string.

(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 Two boxes of fruit on a frictionless horizontal surface are connected by a light string as in the figure below, where m1 = 12 kg and m2 = 24 kg. A force of F = 56 N is applied to the 24-kg block. (a) Determine the acceleration of each block and the tension in the string. acceleration of m1 m/s2 acceleration of m2 m/s^2 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/s^2 acceleration of m2 m/s^2 tension in the string N

Explanation / Answer

F - T = m2a

T = m1a

F - m1a = m2a

a = F/(m1+m2)

a) a1 = F/(m1+m2) = 1.56 m/s^2

a2 = F/(m1+m2) = 1.56 m/s^2

T = m1*a = 18.72 N

b) F - T - u*m2*g = m2*a

T - u*m1*g = m1*a

T = m1*a + um1*g

F - m1*a - um1*g - u*m2*g = m2*a

a = F- u*m1*g - u*m2*g /(m1+m2)

a = 0.58 m/s^2

a1 = a2 = 0.58 m/s^2

T = 18.72 N

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