Question #219022

1. A 6.0 kg mass is connected over a pulley to a 3.0 kg mass. What is the resulting acceleration of the masses when they are released? What is the tension in the string when the masses are released?


1
Expert's answer
2021-07-20T09:46:18-0400

m1=6kgm_1 = 6kg

m2=3kgm_2=3kg

Projection of forces onto the vertical axis:\text{Projection of forces onto the vertical axis:}

m1a=m1g+T-m_1a=-m_1g+T

m2a=m2g+Tm_2a=-m_2g+T

Solution of this system of equations:\text{Solution of this system of equations:}

a=gm1m2m1+m2=9.8636+3=3.27ms2a = g\frac{m_1-m_2}{m_1+m_2}=9.8*\frac{6-3}{6+3}=3.27\frac{m}{s^2}

T=2m1m2gm1+m2=639.86+3=19.6NT=\frac{2m_1m_2g}{m_1+m_2}=\frac{6*3*9.8}{6+3}=19.6N

Answer: a=3.27ms2;T=19.6N\text{Answer: } a = 3.27\frac{m}{s^2};T=19.6N



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