Suppose we have a folding ladder, so that when its legs are spread it makes an isosceles triangle. Suppose it has a support that runs parallel to the ground. There is a bucket of paint that rests on top of the ladder, and the mass of the ladder is negligible.
Data: The legs of the ladder are 2.5m, the separation is 1.3m, and the support is 0.6m, the bucket mass a mass of 20-kg
We are supposed to find the force the support must exert to prevent the ladder from falling.
Torque = r X F
The Attempt at a Solution
We are in static equilibrium so the net torque about the point where one leg hits the floor must be 0.
If you use similar triangles, you should find that the distance from the floor to the support is 1.3462m. I calculated the angle between the left leg and horizontal using trigonometry to be theta = 74.93 degrees. The angle between the vector from the floor to the support and the force of the support is 180 - theta, and the angle between the vector from the floor to the bucket and the force of gravity acting on the bucket is 90 + theta.
I set the sum equal to zero: -mg * 2.5m*sin(90 + theta) + F_support * 1.3462m * sin(180 - theta) = 0. Plug and chug and you get around 98N, but the book gets 57N.
The book has numerous examples with wrong answers, and I have personally emailed the author with agreement that these were errors. Before I jump to conclusions, I want to make sure my calculations aren't in error.