In the Atwood machine shown below, m 1 = 2.00 kg and m 2 = 6.65 kg. The masses o

Question

In the Atwood machine shown below, m1 = 2.00 kg and m2 = 6.65 kg.  The masses of the pulley and string are negligible by comparison. The pulley turns without friction and the string does not stretch.  The lighter object is released with a sharp push that sets it into motion at vi = 2.30 m/s downward.

    (a) How far will m1 descend below its initial level?     
          m     
    
    (b) Find the velocity of m1 after 1.80 s.     
                          

Direction:

magnitude          m/s   In the Atwood machine shown below, m1 = 2.00 kg and m2 = 6.65 kg. The masses of the pulley and string are negligible by comparison. The pulley turns without friction and the string does not stretch. The lighter object is released with a sharp push that sets it into motion at vi = 2.30 m/s downward. How far will m1 descend below its initial level? Find the velocity of m1 after 1.80 s.

Explanation / Answer

a)

F=ma,
(m1-m2)g = (m1+m2)a
a = (m1-m2)g/(m1+m2)
a = -5.27 m/s^
The m1 mass will descend a distance d before it stops (Vf=0). From
Vf^2 - V0^2 = 2ad
d = -V0^2/(2a)
d = 0.854 m
b)

Its speed Vf at t=1.8 is from
Vf - V0 = at
Vf = V0 + at
Vf = 3 + (-5.27)*(1.8)
Vf = -6.49 m/s
m1 is moving up.

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