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Question Ladder Equilibrium ( Physics Help and Math Help - Physics Forums Introductory Physics )
Updated: 2008-11-10 11:40:38 (1)
Ladder Equilibrium

1. The problem statement, all variables and given/known data




A uniform 5.0-kg ladder is leaning against a frictionless vertical wall, with which it makes a 15* angle. The coefficient of friction between ladder and ground is 0.26. Can a 65-kg person climb to the top of the ladder without it slipping? If not, how high can the person climb? If so, how massive a person would make the ladder slip?

2. Relevant equations
LaTeX Code: <BR>\\begin{gathered}<BR>  \\sum {\\vec \\tau }  = \\vec 0 \\hfill \\\\<BR>  \\sum {\\vec F}  = \\vec 0 \\hfill \\\\ <BR>\\end{gathered} <BR>

3. The attempt at a solution

So, I choose the end of ladder that is touching the floor to be the axis. Now I want to find the sum of the torques, then set them equal to zero. What I don't quite get in the equation is the sin(90-15) in the first term in the following equation my professor gave me:

LaTeX Code: <BR>F_W L\\sin (90^ \\circ   - 15^ \\circ  ) - M_p gL\\sin (15^ \\circ  ) - M_L g\\frac{L}<BR>{2}\\sin (15^ \\circ  ) = 0<BR>

sin(90-15)? Technically, it should be the angle between the r and F....but this doesn't make sense to me....or perhaps 15* is meant to be the other angle in the triangle?

If anyone can help, it would be greatly appreciated. Thank you!

Answers: Ladder Equilibrium ( Physics Help and Math Help - Physics Forums Introductory Physics )
Ladder Equilibrium

Hi RedBarchetta,


Originally Posted by RedBarchetta
3. The attempt at a solution

So, I choose the end of ladder that is touching the floor to be the axis. Now I want to find the sum of the torques, then set them equal to zero. What I don't quite get in the equation is the sin(90-15) in the first term in the following equation my professor gave me:

LaTeX Code: <BR>F_W L\\sin (90^ \\circ   - 15^ \\circ  ) - M_p gL\\sin (15^ \\circ  ) - M_L g\\frac{L}<BR>{2}\\sin (15^ \\circ  ) = 0<BR>

sin(90-15)? Technically, it should be the angle between the r and F....but this doesn't make sense to me....or perhaps 15* is meant to be the other angle in the triangle?

Yes, it's the other angle; the ladder makes a 15 degree angle with the wall, so the angle with the floor is 75 degrees. Once you correct your diagram, do you see why the angles your professor chose are correct?

alphysicist

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