Torque and Friction

Question

An 85 kg man is two-thirds the way up a an 8 m ladder that rests against a smooth wall (smooth means no friction) and has a mass of 25 kg and makes an angle with the ground of 50°. Find the force of friction on the ground.

Answer 1

So Benjamin T.,

Did you draw a diagram, label the force vectors, and start by decomposing the man's weight into parallel and perpendicular (to the ladder) components? Do the same for the ladder's weight (it acts from the middle of the ladder). Then it becomes a balance the torques problem. Do torques around the middle of the ladder, so you don't have a torque contribution from the ladder's weight. Remember that the wall is only pushing horizontally, so you must decompose that force, too. When you are done balancing torques, consider the totality of the friction on the ground: it had a perpendicular component to balance the torque, but also a parallel component, to support the ladder along its axis. Add the vectors. As a bonus, you could figure the required coefficient of friction.

-- Cheers, --Mr. d.