Vector torque problem: Force applied to a disc

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Homework Help Overview

The problem involves calculating the torque generated by a force applied to a disk pinned at a point. The disk has a specified radius, and the force's magnitude and application point are given. The discussion revolves around determining the angle between the force vector and the position vector from the pivot point to the point of application.

Discussion Character

  • Conceptual clarification, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the angle between the force vector and the position vector, with initial confusion about the correct angle. There are attempts to clarify the setup by drawing vectors and considering their orientations. Some participants explore the components of the force vector and the position vector to calculate torque.

Discussion Status

The discussion is ongoing, with participants exploring different angles and confirming calculations. There is a collaborative effort to clarify the geometric relationships involved in the problem, and some guidance has been provided regarding the torque calculation.

Contextual Notes

Participants note discrepancies in angle calculations and the need to visualize vector orientations. There is an emphasis on ensuring the correct application of the torque formula, but no consensus has been reached on the final approach to the solution.

jwbensin
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Homework Statement


A force of magnitude 50N is applied at the bottom point Q of a disk of radius 8m that is pinned at P
(leftŸmost point)

See attached picture

(a) Find the angle between the force and the vector from P to Q.
(b) Find the magnitude of the applied torque.

Homework Equations


|T| = |F|sin(Theta)*|r|[/B]

The Attempt at a Solution


So for part (a) I said the angle was 85 degrees but apparently that's wrong? At least according to my colleges online homework program. honestly don't know how to start part (b)
 

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jwbensin said:
So for part (a) I said the angle was 85 degrees but apparently that's wrong?
Draw the vector from P to Q. Then move it so that its tail is at the same point as the tail of the force vector. Now what do you get for an angle between them?
 
You set a usual OXYZ reference system, with origin at point P, and note that the coordinates of point Q are: Q(0,8,-8), and the vector position corresponding to point Q, remains:
r = PQ = <8,-8,0>
Then, note that the components of the force applied at point Q are:
F = <50sin(40º), -50cos(40º), 0>.
Then, to calculate the torque with respect to an axis parallel to the OX axis passing through point P, you have to solve the vector product:
T = r x F.
 
tnich said:
Draw the vector from P to Q. Then move it so that its tail is at the same point as the tail of the force vector. Now what do you get for an angle between them?
95 Degrees?
 
jwbensin said:
95 Degrees?
Yes. Now you have everything you need to substitute into your equation for |T|.
 
tnich said:
Yes. Now you have everything you need to substitute into your equation for |T|.
So would I just simply do |T| = 50sin(95)*8sqrt2 or am I missing something?
 
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jwbensin said:
So would I just simply do |T| = 50sin(95)*8sqrt2 or am I missing something?
I think that would do it.
 

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