Question

A bucket of mass m is hanging from the free end of a rope whose other end is wrapped around a drum (radius R, mass M) that can rotate with negligible friction about a stationary horizontal axis. The drum is not a uniform cylinder and has unknown moment of inertia. When you release the bucket from rest, you find that it has a downward acceleration of magnitude (a). What is the tension in the cable between the drum and the bucket? (b) What is the moment of inertia of the drum about its rotation axis? c) In the primitive yo-yo apparatus (Figure 1), you replace the solid cylinder with a hollow cylinder of mass M, outer radius R, and inner radius R/2. Find the magnitude of the downward acceleration of the hollow cylinder. what is the Tension?

          A bucket of mass m is hanging from the free end of a rope whose
other end is wrapped around a drum (radius R, mass M) that can
rotate with negligible friction about a stationary horizontal axis.
The drum is not a uniform cylinder and has unknown moment of
inertia. When you release the bucket from rest, you find that it
has a downward acceleration of magnitude (a). What is the tension
in the cable between the drum and the bucket? (b) What is the
moment of inertia of the drum about its rotation axis? 
c) In the primitive yo-yo apparatus (Figure
1), you replace the solid cylinder with a hollow cylinder of
mass M, outer radius R, and inner
radius R/2. Find the magnitude of the downward
acceleration of the hollow cylinder. what is the Tension?

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Added by Linda G.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Mahnoor Amin

05/22/2022

Step 1

The forces acting on the bucket are the gravitational force (weight) \( mg \) acting downward and the tension \( T \) in the rope acting upward. Show more…

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A bucket of mass m is hanging from the free end of a rope whose other end is wrapped around a drum (radius R, mass M) that can rotate with negligible friction about a stationary horizontal axis. The drum is not a uniform cylinder and has unknown moment of inertia. When you release the bucket from rest, you find that it has a downward acceleration of magnitude (a). What is the tension in the cable between the drum and the bucket? (b) What is the moment of inertia of the drum about its rotation axis? c) In the primitive yo-yo apparatus (Figure 1), you replace the solid cylinder with a hollow cylinder of mass M, outer radius R, and inner radius R/2. Find the magnitude of the downward acceleration of the hollow cylinder. what is the Tension?

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Transcript

00:01 So let's start with the statement for our version.

00:02 I'd say that there is a bucket of mass m, right? so we have a bucket whose mass is equal to m, right? and it's saying that it's hanging from a free end of the rope whose other end is wrapped around the drum, right? and this is the mass of the bucket, right? and as for the drum, its dimensions are also been given.

00:24 So it has a radius that is equal to r, right? and then it has mass that is equal to capital m.

00:39 Then i say that it can, this bucket, right, it can rotate with negligible friction about the stationary horizontal axis.

00:48 I say that the drum is not a uniform cylinder and has unknown moment of inertia.

00:53 When we release a bucket from the rest, we will find that it has a downward acceleration of magnitude.

01:03 So the first part that we are required to solve over here is the tension, right? tension that is in the cable.

01:15 Fine.

01:17 And it's between the drum and bucket.

01:25 So let's start with the solution for the first part, right, we have a bucket that has a mass m, right? and then we have a drum that has radius r and mass capital m and has downward acceleration.

01:42 Fine.

01:42 So let's start with the tension that is present in the cable between the drum and the bucket.

01:48 Fine.

01:50 Now let d be the tension.

01:54 Right...

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