Torque problem -- friction force on nail between 2 boards

[brake4country]

Could some please help me with this problem?

Boards X and Y are both massless and 4 m in length. A 4 N force is applied to board Y as shown. Board X is held stationary. The two boards are nailed together at 1 m from the left end of board Y. If the boards do not move, what is the static frictional force between the nail and board X?

(A) 4 N
(B) 8 N
(C) 12 N
(D) 16 N

 

[CWatters]

If this is homework it should be in the homework section and you should show your own attempt first.

Hint. Levers.

 

[brake4country]

No, not homework. This is test prep/self-study.

 

[brake4country]

I haven't attempted any math for this problem yet. However, I do know that torque= F x d. My confusion is that the beams are massless. Thanks in advance

 

[A.T.]

My confusion is that the beams are massless.

You don't have to consider the weight of the boards.

 

[jtbell]

No, not homework. This is test prep/self-study.

It doesn't matter. If you're trying to find the solution for a specific exercise like this, we consider it "homework-like" and it belongs in the homework forums.

You've already received some help, and you've used the appropriate forum before, so I'll simply move this there.

 

[CWatters]

I haven't attempted any math for this problem yet. However, I do know that torque= F x d. My confusion is that the beams are massless.

So ignore the mass. What other forces or torques must exist in addition to the applied 4N ? Are the beams moving? Accelerating? What does that imply?

 

[Ry122]

fulcrum of rotation is at the end of board y
4Newtons * 4metres = 16N*m

T=F*S
where s = 1
16=F*1
F=16Newtons

 

[CWatters]

Ry122. Please see...

https://www.physicsforums.com/showthread.php?t=414380

Homework Help Guidelines

On helping with questions: Any and all assistance given to homework assignments or textbook style exercises should be given only after the questioner has shown some effort in solving the problem. If no attempt is made then the questioner should be asked to provide one before any assistance is given. Under no circumstances should complete solutions be provided to a questioner, whether or not an attempt has been made.

 

[brake4country]

Okay. I am slowly understanding this problem but I still need some clarification...

My understanding of torque as a static problem requires the sum of all torques must equal zero. So, initially, I set the problem up as:

T (clockwise) = T (counterclockwise)

My initial question was: why can't the nail be a point of rotation? Now I realize that the nail exerts a force, therefore, it cannot be a point of rotation. If the point is chosen to be at the end of y, then:

T (clockwise) = T (counterclockwise)

F (1 m) = (4 N) (4 m)
F = 16 Nm

Is this an accurate way to express the equation?

 

[CWatters]

That all look fine to me.

You could pick the nail as the point of rotation about which to sum the torques.. but you would then have to take into account other torques such as the force that board Y applies on board X at the left hand end of Y (and that's not known).

In general.. if there is an unknown force in a problem try putting the point of rotation there so that it's taken out of the equation (eg T=F*d but d=0)