Calculating Forces on Ladder and Nail in 60-degree Angle

[willydavidjr]

A uniform ladder with a mass of 10 kg leans against a vertical, smooth

wall making an angle of 60 degrees with a smooth floor as shown in

diagram ( I provided the website:

www.geocities.com/willydavidjr/ladder.html ) A nail in the floor keeps

the ladder from slipping while a man (mass = 80 kg) climbs

three-quarters of the way to the top. THe frictional force of the head

of the nail (i.e. the section above the floor) is negligible.

Let the gravitational acceleration be 10 m/s^2 and the value of

squareroot of 3 = 1.73.

a.) Calculate the magnitude of the force exerted on the wall.
b.) Calculate the magnitude of the force exerted on the smooth floor.
c.) Calculate the magnitude of the horizontal force exerted on the

nail.


My work: I am really confused with this problem. First I tried the summation of torque be equal to zero, but the problem is, I don't know the height of the wall where the ladder is leaning, and the ladder itself has no distance. What is the connection of the man climbing 3/4 up to the ladder. Please help me and give me advice with these.

 

[Doc Al]

What matters is the angle, which you are given, not the length of the ladder. (Hint: Call the length of the ladder L; it will drop out of any torque equation you use.) In addition to setting the sum of the torques about any point equal to zero, don't forget that the sum of the forces on the ladder must also equal zero for equilibrium to hold.

 

[willydavidjr]

Ok I'll try again. But it seems I already did what you said and didn't work. I think I am missing something here.