Thank YOU for looking at myquestion! M 1 and M 2 are two masses connected asshow

Question

Thank YOU for looking at myquestion!
M1 and M2 are two masses connected asshown.

http://tinypic.com/r/30aupw3/6

The pulley is light (massless) and frictionless. Find the massM1, given that M2 (4.5 kg) acceleratesdownwards at 2.99 m/s2, Theta is 30o,and k is 0.25. Cheers Thank YOU for looking at myquestion!
M1 and M2 are two masses connected asshown.

http://tinypic.com/r/30aupw3/6

The pulley is light (massless) and frictionless. Find the massM1, given that M2 (4.5 kg) acceleratesdownwards at 2.99 m/s2, Theta is 30o,and k is 0.25. Cheers Cheers

Explanation / Answer

The equation of motion is F= m2g - f - Fd Force of friction f = m1gcos(30) Downward force ofm1    Fd=m1gsin(30) we have a(m1 + m2) =m2g -m1gcos(30) - m1gsin(30) am1 +m1gcos(30)+m1gsin(30) =m2g - am2 Now solving for m1 Now solving for m1 a) m1= m2[g - a]/[a + gcos(30)+gsin(30) ]
          =4.25*(9.8 -2.99)/ (2.99 + 0.25*9.8*0.866+9.8*0.5 )
         =2.89kg

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