Finding the Critical Angle for Shelf Gliding: A Statics Problem

[NathalieSweden]

Homework Statement

Excuse my english, it is not my first language.
A bookcase has the weight 1500N and is standing at a horizontal floor. The friction force between the floor and the shelf is 600N.
The shelf's height is 1,8mand it is 2m wide. The shelf stands on four feet each 0,01m from the edge. The masscentre is located at the middle of the shelf. A person pulls at the top of one of the shelf's edges. The force creates an angle v with the shelf's side.

I have to form an expression for when the shelf starts gliding, as a function of the angle v.
I will add a file with a pictur that explains the situation.

Homework Equations

torque, T=Fxr
Friction, Ff=uN

The Attempt at a Solution

I have calculated the force needed to tip the shelf at v=90degrees: 13500N. Also the force needed to make the shelf start gliding when v=0(paralell)=600N. The force needed to tip the shelf at v=0 is 750N
I have no idea how to form the function.

 

[NathalieSweden]

Oops I posted the image twice...

 

[BvU]

Hello Sweden, welcome to PF :)

My swedish is good enough to see a $\mu_s=0.4$.
The friction force is $F_f = \mu_s * F_N$.
$F_N$ is the net normal force that compensates mg and the vertical component of the pulling force F
So $F_f = 600$ N is only when pulling force F is horizontal ($\theta = {\pi\over 4}$ ), which is given in part a).

Were does the 13500 N come from ? Probably part b) 1.9 * 1500 = 0.1 * F
[edit] yes of course, 0.9

ANd you want some function of $\theta$ in part c). That means you have to decompose F in horizontal and vertical components. What kind of function is wanted, my limited swedish doesn't reveal me, so perhaps you want to describe it a bit more extensively ...

 

[NathalieSweden]

Yes it comes from b). But it's: 0,1F*0,9*1500. This is correct, the teacher has passed me on a) and b).
Yes that is true. Determine the x and y directed forces for when the shelf glides and tips. Then I am supposed to find the minimum angle where the shelf starts gliding instead of tipping. Do you understand what I mean?

 

[BvU]

"Determine the x and y directed forces for when the shelf glides and tips"

I can't make sense out of that. Can you ? If so, show some steps and indicate where you run into problems...