M,RA pulley with radius R and moment of inertia about its central axis 1/2 MRis mounted on frictionless bearing. A massless cord is wrapped around thepulley with mass m attached on one side and massless spring with springconstant k on another side. The spring is connected to the ground. Corddoes not slip on the pulley. Find acceleration of the box at the point at whichthe spring is maximally stretched (at this point the block instantaneouslystops).т

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Asked Dec 9, 2019
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M,R
A pulley with radius R and moment of inertia about its central axis 1/2 MR
is mounted on frictionless bearing. A massless cord is wrapped around the
pulley with mass m attached on one side and massless spring with spring
constant k on another side. The spring is connected to the ground. Cord
does not slip on the pulley. Find acceleration of the box at the point at which
the spring is maximally stretched (at this point the block instantaneously
stops).
т
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M,R A pulley with radius R and moment of inertia about its central axis 1/2 MR is mounted on frictionless bearing. A massless cord is wrapped around the pulley with mass m attached on one side and massless spring with spring constant k on another side. The spring is connected to the ground. Cord does not slip on the pulley. Find acceleration of the box at the point at which the spring is maximally stretched (at this point the block instantaneously stops). т

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Expert Answer

Step 1

the tension on the right side is T1 and left side is T2 which is nothing but the restoring force,

the magnitude of restoring force is kx, x is the stretched length by the spring,

Step 2

the expression for the torque on the pulley is, 

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T= (T, -T,)R I@= (T,-T,) R MR? -@ = (T,-T; )R·: @ =. ais the linear acceleration MR ( a =(T-T, )R 2 R Ma Т, -т, Ma T- kx =: 2 ||

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Step 3

on the right side the, equilibr...

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1 -mg = -ma 1 = mg - ma

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