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Three masses m 1 , m 2 and m 3 are being pulled by force F (Figure). Strings connecting m 1 to m 2 and m 2 to m 3 are massless. The coefficient of kinetic friction between masses and table is 0.1. If m 1 = 20 kg, m 2 = 30 kg and m 3 = 50 kg and F-1500N then (a) What is the acceleration of books? (b) What are the tensions in strings tied between m 1 and m 2 and m 2 and m 3 ?

Three masses m1, m2 and m3 are being pulled by force F (Figure). Strings connecting m1 to m2 and m2 to m3 are massless. The coefficient of kinetic friction between masses and table is 0.1. If m1 = 20 kg, m2 = 30 kg and m3 = 50 kg and F-1500N then


1418_88597_Image~ 1.jpg


(a)    What is the acceleration of books?


(b)    What are the tensions in strings tied between m1 and m2 and m2 and m3?

Grade:upto college level

1 Answers

Radhika Batra
247 Points
7 years ago

Let T1 = Tension in the string tying m1 to m2.

and T2 = Tension in the string tying m2 to m3.

Free body diagram for the masses and corresponding equations are

T1–µkm1g = M1a

T2–T1–µkm2g = m2a

F–T2–µkm3g = m3a

818_88598_Image~ 1.jpg

Solving these equations we get

(a)    m3a = F–µkg(m1+m2+m3)–m1a–m2a

1018_88598_Image~ 1.jpg

= 14.02 m/s2

(b)    T1 = m1 a + m1 µk g

T1 = 20 (14 + 0.98) = 299.60 N

T2 = 299.60 + 30 × 14.98 = 749 N

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