How to Find the Angular Acceleration of a Falling Post?

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Homework Help Overview

The problem involves a thin, uniform post that is held vertically and supported by a cable. The scenario describes the dynamics of the post and a hanging mass when the cable snaps, prompting questions about angular acceleration and the behavior of the system immediately after the cable breaks.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the calculation of torque and moment of inertia to find angular acceleration. There are attempts to understand why the angular acceleration might not be constant and the implications of the mass's acceleration on the tension in the string.

Discussion Status

Some participants are exploring the relationship between the forces acting on the post and the hanging mass, questioning the assumptions about tension in the string and its dependence on the mass's acceleration. There is an ongoing examination of the calculations and reasoning behind the expected answers.

Contextual Notes

Participants note the lack of a diagram and specifics about the pulley attachment, which may affect the interpretation of the problem. The discussion includes uncertainty about the nature of the forces involved and how they change as the system evolves after the cable snaps.

C.E
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1. Hi, I am massively stuck on the following question and am examined on this stuff soon, could someone please help me?

A thin, uniform 15kg post of length 1.75 m is held vertically using a cable attached to the top of the post. A string attached to a 5kg mass passes over a smooth, massles pulley and is attached to the post 0.5m from the top. The post has a pivot at the bottom of it (i.e. that is what it rests on). Suddenly the cable snaps.

a. Find the angular acceleration of the post (with respect to the pivot) just after the cable snaps.
b.Will the angular acceleration from a be constant before the post hits the pulley? Why?
c.What is the acceleration of the 5kg mass the instant the pulley breaks? Is this constant? Why?

b[2].According to the back of my book the answers I should get are:
a. 2.65 rad/s^2
b. no, no explanation why given.
c. 3.31 m/s^2, n (no explanation given)

b[3].My attempt.
a. Torque (T)= moment of inertia (I) x angular acceleration (A)
T= 5g(1.75-0.5)=61.25
I= (MR^2)/4 = 15.3125
a=T/I = 4
(I don't see where I am going wrong for this part, any ideas?)
b. I think no because as the stick falls the line of action of the applied force changes and hence so does the torque. Is this explanation correct?
c. I though this acceleration was just g. As for whether it is constant I thought yes, but the answer is no.
 
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C.E said:
A thin, uniform 15kg post of length 1.75 m is held vertically using a cable attached to the top of the post. A string attached to a 5kg mass passes over a smooth, massles pulley and is attached to the post 0.5m from the top.
A diagram would help. What's the orientation of the string? What's the pulley attached to?
 
C.E said:
b[3].My attempt.
a. Torque (T)= moment of inertia (I) x angular acceleration (A)
T= 5g(1.75-0.5)=61.25
I= (MR^2)/4 = 15.3125
a=T/I = 4
(I don't see where I am going wrong for this part, any ideas?)
Hint: Find the tension in the string once the cable is cut. It's not simply equal to the weight of the 5kg mass.

(Assuming the string is horizontal, I get the book's answer.)
 
Yes, the string is horizontal. It does not say anything about what the pully is attached to. Why is the tension not just 5g? What am I missing?
 
C.E said:
What am I missing?
The fact that the mass accelerates.
 
What do you mean?
 
C.E said:
What do you mean?
The tension in the string will equal the weight of the hanging mass when the mass is stationary (not accelerating). (mg - T = 0) But when the mass starts accelerating, the string tension is less. (mg - T = ma)
 

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