Physics 123 Quizes and Examinations Spring 2007 Porter Johnson ...

Determine the maximum tilt angle θ at which the ladder can be in staticequilibrium.Solution:The force F produced by the wall on the ladder is out of the wall, whereasthe static friction f s at the base is toward the wall. The weight W is downwardat the center of the ladder, whereas the normal force N at the base ofthe ladder is upward. For equilibrium, F = f s and N = W = m g.We also require that the net torque about the base of the ladder is zero. Thenormal force N and static friction f s produce no torque at this point. Theforce F produces a torque that would cause the ladder to rotate away fromthe wall, whereas the weight produces a torque to cause rotation toward thewall. We obtainF L cos θFor the critical case f s = µ s N, so thatF= m g L 2 sin θ= m g2 tan θm g2 tan θ = m gtan θ = 2µ s = 0.3θ = 17 o14. PHYS 123 - 052 QUIZ 7 26 April 2007One end of a uniform beam of mass m = 20 kilograms and length L = 1meter is attached to a wall with a hinge. The beam hangs at an angle θ = 30 obelow the horizontal direction. The other end of the beam is supported bya light wire, which is attached to the wall above the beam. The wire makesan angle φ = 30 o with the vertical direction.• Find the tension T in the wire.• What are the horizontal H and vertical V components of the force atthe hinge?Solution: