A cylindrical pulley with a mass of 8 kg, radius of 0.561 m and moment of inertia 1 2 M r2 is used to lower a bucket with a mass of 1.9 kg into a well. The bucket starts from rest and falls for 2.6 s. r M m How far does it drop

s = 15.84m

Explanation:

In order to calculate the distance traveled by the bucket, you first use the formula for the torque exerted on the pulley by the weight of the bucket:

       (1)

I: moment of inertia of the pulley

α: angular acceleration of the pulley

You can calculate the angular acceleration by taking into account that the torque is also:

    (2)

W: weight of the bucket = Mg = (1.9kg)(9,8m/s^2) = 18.62N

r: radius of the pulley = 0.561m

The moment of inertia is given by:

    (3)

Mp: mass of the pulley = 8kg

You solve the equation (1) for α and replace the values of the moment of inertia and the torque to obtain the angular acceleration:

Next, you use the following formula to find the angular displacement:

Finally, you calculate the arc length traveled by the pulley, this arc length is equal to the vertical distance traveled by the bucket:

The distance traveled by the bucket is 15.84m