Question

A 2.80kg bucket is attached to a disk-shaped pulley of radius 0.151m and mass 0.742kg . If the bucket is allowed to fall,

What is its linear acceleration?

What is the angular acceleration of the pulley?

How far does the bucket drop in 1.00s ?

Answer 1

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A 2.80 kg bucket is attached to a disk-shaped pulley of radius 0.151 m and mass 0.742 kg. If the bucket is allowed to fall,

What is its linear acceleration?


What is the angular acceleration of the pulley?


How far does the bucket drop in 1.20s ?

answer

Mass of the bucket ( M ) = 2.8kg

Radius of the disc ( r ) = 0.151 m

Mass of the pulley ( m ) = 0.742 kg

Time ( t ) = 1.20 s

..................................................................................................

Form newtons law , net force

mg - T = ma

T ( r ) = ( I ) ? = (Mr²/2) (a/r), so T = Ma/2

mg - Ma/2 = ma

Therefore acceleration ( a ) = mg / (M/2 + m)

                                          = ( 0.742 kg ) ( 9.8 m/s² ) / ( 1.4 kg ) + 0.742  

                                         = 3.394 m/s²

........................................................................................................................

angular acceleration of the pulley ? = a/r

                                              = ( 3.394 m/s² ) / 0.151 m

                                             = 22.48 rad/s²

..............................................................................................................................

distance at 1.20 s = at²/2

                            = ( 3.394 m/s² ) ( 1.20 s) ² / 2

                          = 2.443 m