Question

A cylindrical pulley with a mass of 4.7 kg, radius of 0.961 m and moment of inertia 1 2 M r2 is used to lower a bucket with a mass of 1.7 kg into a well. The bucket starts from rest and falls for 2.7 s. r M m What is the linear acceleration of the falling bucket

Answer 1

Step-by-step explanation:

Given

Mass of Pulley
`M=4.7\ kg`

radius of Pulley
`r=0.961\ m`

mass of bucket
`m=1.7\ kg`

Time period of fall
`t=2.7\ s`

Tension in the string is T

For bucket
`mg-T=ma-------1`

For Pulley Tension will provide Torque to rotate it

`T\cdot r=I\itmes \alpha`

where I=moment of inertia

`\alpha`=angular acceleration

r=radius of Pulley

assuming rolling
`a=\alpha * r`

`T\cdot r=(Mr^2)/(2)\cdot r`

`T=(Ma)/(2)`

Substitute the value of Tension in equation 1

`mg-(Ma)/(2)=ma`

`a=(mg)/(m+0.5M)`

`a=(1.7* 9.8)/(1.7+0.5\cdot 4.7)`

`a=4.11\ m/s^2`