3- The drawing shows a systems of objects; which consists of three small balls c

Question

3- The drawing shows a systems of objects; which consists of three small balls connected by massless rods. The axis is perpendicular to the page as shown. The force of magnitude F is applied to the m2 ball (see the drawing). The masses of the balls are1 -900 kg, m2 -600 kg, and3 7.00 kg. The magnitude of the force is F = 424 N. 1 3.00m2 m1 3.00mm2 Axis 4.00 m 4.00 m 5.00 m 5.00 m Axis n13 m3 System A System B Determine the moment of inertia about the given axis of rotation. Calculate the torque magnitude acting on the system. The systems start from rest, and the direction of the force moves with the system and always points along the 4.00-m rod. What is the angular velocity of the system after 5.00 s? If we change the axis to m2 ball as shown. Determine the moment of inertia about the given axis of rotation. Calculate the torque magnitude acting on the system. a. b. c. d.

Explanation / Answer

a)We kow that for a point mass

I = m r^2

for A

IA = m1 x 0^2 + m2 x 3^2 + m3 5^2

IA = 0 + 6 x 9 + 7 x 25 = 229 kg-m^2

Ib = m1 5^2 + m2 4^2 + m3 x 0^2

IB = 9 x 25 + 6 x 16 + 0 = 321 kg-m^2

Hence, IA = 229 kg-m^2 ; IB = 321 kg-m^2

b)For A

Tau-A = 424 x 3 = 1272 N-m

Tau-B = 424 x 0 = 0 N-m

Hence, Tau-A = 1272 N-m(= -1272 N-m) and Tau-B = 0 N-m

c)We know that

alpha = Tau/I = 1272/229 = 5.55 rad/s^2

from eqn in circular motion

wA = 0 + 5.55 x 5 = 27.75 rad/s

wB = 0 rad/s

Hence, wA = 27.75 rad/s ; wB = 0 rad/s

b)I = m1 3^2 + m3 4^2 + m2 x 0^2

I = 9 x 9 + 7 x 16 = 193 kg-m^2

Hence, I = 193 kg/m^2

tau = 0

since r = 0

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