What Is the Acceleration of a Cord Wrapped Around a Disk?

[Shhtory]

A cord is wrapped around a homogeneous disk of radius r = 0.5 m and mass 29 kg, as shown in Fig. 2 "Cord around disk". The cord is pulled upwards with a force T of magnitude 148 N, with gravity acting vertically downwards. Determine the acceleration of the cord, in m/s2, positive if upwards

Homework Statement

radius r = 0.5 m
mass 29 kg
force T=148 N

Homework Equations

a=(T/m)+(T/r)-g

The Attempt at a Solution

a=(148/29)+(148/0.5)-9.81
a = 291.293

Just not 100% sure about this one and if I'm on the right track, would really appreciate the help! xx

 

[KataKoniK]

Thank you for your post. I am a scientist and I would be happy to assist you with this problem.

Firstly, I would like to clarify a few things about the given information. When you say "cord around disk", I assume that the cord is wrapped around the circumference of the disk and is attached to a fixed point above the disk. Also, I assume that the disk is on a horizontal surface and is not rotating.

Now, let's look at the forces acting on the disk. We have the tension force T pulling upwards and the gravitational force mg acting downwards. Since the cord is wrapped around the disk, the tension force is also acting tangentially on the disk. This means that the net force acting on the disk is the vector sum of T and mg, which can be represented as:

Fnet = T + mg

Using Newton's second law of motion, we can write:

Fnet = ma

Substituting for Fnet, we get:

ma = T + mg

Solving for the acceleration, we get:

a = (T + mg)/m

Substituting the given values, we get:

a = (148 + 29*9.81)/29 = 14.6 m/s^2 (upwards)

Therefore, the acceleration of the cord is 14.6 m/s^2 upwards.

I hope this helps. Let me know if you have any further questions.