(Figure 1) illustrates an Atwood\'s machine. Let the masses of blocks A and B be
ID: 1461189 • Letter: #
Question
(Figure 1) illustrates an Atwood's machine. Let the masses of blocks A and B be 9.00 kg and 1.00 kg , respectively, the moment of inertia of the wheel about its axis be 0.220 kg?m2, and the radius of the wheel be 0.120 m. There is no slipping between the cord and the surface of the wheel. (please include units)
A) Find the magnitude of the linear acceleration of block A
B) Find the magnitude of linear acceleration of block B.
C) Find the magnitude of angular acceleration of the wheel C.
D) Find the tension in left side of the cord.
E) Find the tension in right side of the cord.
Explanation / Answer
Let a is the acceleration of two blocks
Let TL and TR are the tensions in the left and right cord.
A) net force acting on block A, FnetA = mA*g - TR
mA*a = mA*g - TR
TR = mA*g - mA*a ---(1)
Net force acting on block B, FnetB = TL - mB*g
mB*a = TL - mB*g
TL = mB*g + mB*a --(2)
Net torque acting on pulley, Tnet = I*alfa
TR*R - TL*R = I*a/R
TR - TL = I*a/R^2
mA*g - mA*a - (mB*g + mB*a) = I*a/R^2
g*(mA - mB) - a*(mA + mB) = I*a/R^2
g*(mA - mB) = I*a/R^2 + a*(mA + mB)
g*(mA - mB) = a*(I/R^2 + mA + mB)
a = g*(mA - mB)/(I/R^2 + mA + mB)
= 9.8*(9 - 1)/(0.22/0.12^2 + 9 + 1)
= 3.1 m/s^2 (downward) <<<<<<-----------Answer
B) acceleration of block B = 3.1 m/s^2 (upward)
c) alfa = a/R
= 3.1/0.12
= 25.83 rad/s^2
D) from equation 2
TL = mB*g + mB*a
= 1*9.8 + 1*3.1
= 12.9 N
E) from equation 1
TR = mA*g - mA*a
= 9*9.8 - 9*3.1
= 60.3 N
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.