(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

There is a sliding door lifted at a constant rate by two cables, A and B. The sides of the door fit loosely into grooves in the walls.

Dimensions of door: 9 ft tall by 10 ft wide

Weight of the door: 200 lbs

Cable A is attached at the top of the door, 2 ft from the left side

Cable B is attached at the top of the door, 2 ft from the right side

The coefficient of kinetic friction between the door and grooves is 0.3

Suppose cable B breaks. What force must cable A exert to continue raising the door at a constant rate?

2. Relevant equations

Equilibrium equations:

[tex]\sum[/tex]F_{x}= 0, [tex]\sum[/tex]F_{y}= 0, [tex]\sum[/tex]M = 0

Friction equation (N is force normal to surface):

f=[tex]\mu[/tex] * N

3. The attempt at a solution

It seems as if I don't have enough information to solve the problem.

To highlight the difficulty I have chosen to sum the moments about the center of mass of the door.

[tex]\sum[/tex]F_{x}= N_{left}- N_{right}= 0

[tex]\sum[/tex]F_{y}= T_{A}- 200 - (.3)N_{left}- (.3)N_{right}= 0

[tex]\sum[/tex]M = 5*0.3*N_{left}- 5*0.3*N_{right}- 3*T_{A}= 0

What I immediately discover is that the two normal forces are equal, and therefore from the last equation T_{A}= 0. Obviously this is not the correct answer!

I thought that perhaps I could add a couple to the final equation to reflect the fact that the unbalanced door is trying to rotate and can't due to the door frame, but then I end up with four unknowns :-/

What am I missing about this problem?

Thanks,

-Zac

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# Homework Help: Equilibrium problem: sliding door

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