As shown on Figure below, Atwood's Machine consists of two masses, m, and m2, i.e., m, > m, suspended from a pulley that is attached to the ceiling. The sizes of the blocks are ignored in all cases. The pulley is a thin disk of mass M and radius R. Do NOT ignore the motion of the pulley in this problem. The tension T, is in the rope pulling on mass m, and the tension T; is in the rope pulling on mass m2. a) Using the Newton's second law, write expressions M for the two masses and the pulley. You can use the R unknown tensions T, and Tz in your expression. Be sure to explicitly indicate your chosen coordinate T2 axes in all cases. b) Mass m, starts from rest a distance h above the m2 floor. Find a, the linear acceleration of the blocks. (Hint: the angular acceleration of the pulley determines how fast the blocks move.) c) At what speed does m, hit the floor? d) What is the rotational speed of the pulley just as m, hits the floor? mi

Question
As shown on Figure below, Atwood's Machine consists of two masses, m, and m2, i.e., m, > m,
suspended from a pulley that is attached to the ceiling. The sizes of the blocks are ignored in all
cases. The pulley is a thin disk of mass M and radius R. Do NOT ignore the motion of the pulley in
this problem. The tension T, is in the rope pulling on mass
m, and the tension T; is in the rope pulling on mass m2.
a) Using the Newton's second law, write expressions
M
for the two masses and the pulley. You can use the
R
unknown tensions T, and Tz in your expression. Be
sure to explicitly indicate your chosen coordinate
T2
axes in all cases.
b) Mass m, starts from rest a distance h above the
m2
floor. Find a, the linear acceleration of the blocks.
(Hint: the angular acceleration of the pulley
determines how fast the blocks move.)
c) At what speed does m, hit the floor?
d) What is the rotational speed of the pulley just as m,
hits the floor?
mi

Image Transcription

As shown on Figure below, Atwood's Machine consists of two masses, m, and m2, i.e., m, > m, suspended from a pulley that is attached to the ceiling. The sizes of the blocks are ignored in all cases. The pulley is a thin disk of mass M and radius R. Do NOT ignore the motion of the pulley in this problem. The tension T, is in the rope pulling on mass m, and the tension T; is in the rope pulling on mass m2. a) Using the Newton's second law, write expressions M for the two masses and the pulley. You can use the R unknown tensions T, and Tz in your expression. Be sure to explicitly indicate your chosen coordinate T2 axes in all cases. b) Mass m, starts from rest a distance h above the m2 floor. Find a, the linear acceleration of the blocks. (Hint: the angular acceleration of the pulley determines how fast the blocks move.) c) At what speed does m, hit the floor? d) What is the rotational speed of the pulley just as m, hits the floor? mi

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