three masses m1,m2 and m3 are being pulled by a force F from the side of m1.strings connecting m1 to m2 and m2 to m3 are mass less. the coffecient of kinetic friction between the masses and the table is 0.1.if m1=20kg,m2=30kg and m3=50kg and F=1500N then (i)what is the acceleration of the masses?(ii)what are the tensions in the string between m1 &m2 and m2 &m3?

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Solution

$(i) Net force : F_{net} = F - μ (m_{1} + m_{2} + m_{3}) g = 1500 - [(0.1) (20 + 30 + 50) 9.8] = 1500 - 98 = 1402 N Acceleration : a = \frac{F_{net}}{m_{1} + m_{2} + m_{3}} = \frac{1402}{20 + 30 + 50} = 14.02 m / s^{2} (ii) Tension between m_{1} and m_{2} : F - T_{1} - {μm}_{1} g = m_{1} a T_{1} = F - {μm}_{1} g - m_{1} a = 1500 - (0.1 \times 20 \times 9.8) - (20 \times 14.02) = 1200 N Tension between m_{2} and m_{3} : F - T_{2} - μ (m_{1} + m_{2}) g = (m_{1} + m_{2}) a T_{2} = F - μ (m_{1} + m_{2}) g - (m_{1} + m_{2}) a = 1500 - (0.1 \times 50 \times 9.8) - (50 \times 14.02) = 750 N$

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