A mother pushes her two children on a 200kg Merry-go-round of radius R=6m. Child

Question

A mother pushes her two children on a 200kg Merry-go-round of radius R=6m. Child 1 (m1=25kg) sits in a seat a distance of r1=3m from the axis of rotation. Child 2 (m2=35kg) sits in a seat a distance of r2=5m from the axis of rotation. The mother pushes with a maximum force of 300N at the edge of the merry-go-round. Assume the merry-go-round to be a uniform circle ( I = 1/2MR^2) and treat children as point masses

a) (10pts) Determine the center of mass of this system (children + merry-go-round) at the instant shown in the diagram above. Assume the origin (0,0) is at the axis of rotation.

b) (10pts) Determine the moment of inertia of the system.

c) (5pts) What is the angular acceleration of the merry go round, assuming no friction?

d) (5pts) What is the angular acceleration of the merry-go-round if you include a frictional torque of 300N-m?

e) (5pts) The outermost child falls off the merry-go-round at an angular velocity of 5rad/s, and the mother stops pushing to help the child. Assuming the same frictional torque from part (d), how long does it take the merry-go-round to stop turning?

Explanation / Answer

let cm be at x from centre so x*(m1+m2+M)=m1r1-m2r2 so x=-.38 m from the centre a)so CM at -.38 from centre towards 35 kg baby b)I=.5*M*R^2 +m1*r1^2+m2*r2^2=4700 kg-m^2 c) angacc=Torque/I=Fmom*R/I=.383 rad/s^2 d)angacc2=Torque2/I=(300*6-300)/I=.32 rad/s^2 e)

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