How can I determine the required force to balance a pivoted metal sheet?

[controlfreaks]

Homework Statement

A thin sheet of metal is pivoted at one corner (the origin) and it's free to rotate about the origin in the xy plane. It has sides of 1.6m and 1.2m. two forces f and -Mgj are acting on the sheet of metal. f acts parallel to the x-direction (in the minus direction) and -Mg is the force due to gravity which acts downwards through the centre of the metal sheet. Find the total torque at origin due to these forces and hence determine what for what force f the sheet metal is balanced so that it does not rotate around the pivot point when the sheet has a mass of 0.5Kg.

Homework Equations

T=r.f
Torque is the force applied by the distance from the pivot point in this case.

The Attempt at a Solution

using pythagorus i get that f acts at 4 units away from the origin and -Mg acts at 2 units away. I can calulate the torque that -Mg is applying but no value is given for the force f so i cannot add these together. Help please!

 

[kuruman]

Is the point on the sheet at which f acts given? Also, what is the orientation of the sheet relative to the vertical? A drawing would help.

 

[semc]

I don't quite understand the question but what i think is a metal plate is pivoted on 1 corner and a force f is acting on the other corner of the plate right? If that is the case then i think, the question ask you to find the force f the sheet metal is balanced so just use the equation and equate both of them together since the sheet is balanced. Btw the distance i got was 2 and 1 from the corner of the sheet.

 

[kuruman]

If the point on the sheet where f acts is not given, then the problem is incomplete. The torque f generates cannot be found without this information. The closer that point moves to the pivot, the larger a force you will need to balance the sheet. Is there a drawing or just the description that you gave?

 

[controlfreaks]

yes the point that f acts on is the opposite point to the origin. and it's pushing in at the rectangle in the minus x direction.

the question definatly asks to find the total torque at point O and hence THEN find the balancing f required.

do i take it that the answer to the first part must be given in terms of f? and the second part is where you let them equal as mentioned above?

 

[kuruman]

And how is the rectangular sheet oriented? Is the long side 1.6 m along the x-axis or along y? In other words is the point of application of f (1.6 m, 1.2 m) or (1.2 m, 1.6 m)?

 

[controlfreaks]

the long side is along the x-axis and the sheet is in the xy plane.

 

[kuruman]

OK. So now you need to calculate two torques, one due to gravity and one due to f. How would you do that?

 

[controlfreaks]

i know how to calculate the torques but the force applied by f is not given, that's why I'm wondering if the answer should be givin in terms of f?

 

[kuruman]

Yes. Use symbol f in the equation of torque balance and then solve for it in terms of M, g and the dimensions of the sheet.

 

[controlfreaks]

perfick, thanks guys!