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?
m1=6kgm_1 = 6kgm1=6kg
m2=3kgm_2=3kgm2=3kg
Projection of forces onto the vertical axis:\text{Projection of forces onto the vertical axis:}Projection of forces onto the vertical axis:
−m1a=−m1g+T-m_1a=-m_1g+T−m1a=−m1g+T
m2a=−m2g+Tm_2a=-m_2g+Tm2a=−m2g+T
Solution of this system of equations:\text{Solution of this system of equations:}Solution of this system of equations:
a=gm1−m2m1+m2=9.8∗6−36+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}a=gm1+m2m1−m2=9.8∗6+36−3=3.27s2m
T=2m1m2gm1+m2=6∗3∗9.86+3=19.6NT=\frac{2m_1m_2g}{m_1+m_2}=\frac{6*3*9.8}{6+3}=19.6NT=m1+m22m1m2g=6+36∗3∗9.8=19.6N
Answer: a=3.27ms2;T=19.6N\text{Answer: } a = 3.27\frac{m}{s^2};T=19.6NAnswer: a=3.27s2m;T=19.6N
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