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

Answer:

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 $a=\alpha \times r$

$T\cdot r=\frac{Mr^2}{2}\cdot r$

$T=\frac{Ma}{2}$

Substitute the value of Tension in equation 1

$mg-\frac{Ma}{2}=ma$

$a=\frac{mg}{m+0.5M}$

$a=\frac{1.7\times 9.8}{1.7+0.5\cdot 4.7}$

$a=4.11\ m/s^2$