Answer to Question #219022 in Classical Mechanics for Laura

Question

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?

Answer 1

$m_1 = 6kg$

$m_2=3kg$

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

$-m_1a=-m_1g+T$

$m_2a=-m_2g+T$

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

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

$T=\frac{2m_1m_2g}{m_1+m_2}=\frac{6*3*9.8}{6+3}=19.6N$

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