Two blocks on a frictionless horizontal surface are connected by a light string,

Question

Two blocks on a frictionless horizontal surface are connected by a light string, where m1 = 11 kg and m2 = 29 kg. A force of 70 N is applied to the 29 kg block.

(a) Determine the acceleration of each block and the tension in the string.
____m/s^2 (acceleration of m1)
____m/s^2 (acceleration of m2)
____N (tension in the string)
(b) Repeat the problem for the case where a coefficient of kinetic friction between each block and the surface is 0.1.
____m/s^2 (acceleration of m1)
____m/s^2 (acceleration of m2)
____N (tension in the string)

Explanation / Answer

a)
Acceleration a= F/(m1 + m2) = 70/(11+29) = 1.75 m/s^2
Acceleration of block 1 = acceleration of block 2 = 1.75 m/s^2
Tension in string = m1*a = 11*1.75 = 19.25 N

b)
friction force f = (m1+m2)g = 0.1 * (11+29) * 9.8 = 39.2 N
Acceleration of block1 = acceleration of block2 = (F-f)/(m1 + m2) = (70-39.2)/(11+29) = 0.77 m/s^2
Tension in string = m1*g + m1*a = 0.1*11*9.8 + 11*0.77 = 19.25 N

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