A 5.0-m long, 15-kg uniform ladder rests against a smooth vertical wall with the bottom of the ladder 3.0 meters from the wall. The coefficient of static friction between the floor and the ladder is 0.28. What distance (d), measured along the ladder from the bottom, can a 60.0 kg person climb before the ladder starts to slip? Hint: the center of gravity of the latter is at its geometry center. Show all work including but not limited to coordinate system, equations along the axis, free body diagrams and torque diagrams. u = 0.28

A 5.0-m long, 15-kg uniform ladder rests against a smooth vertical wall with the bottom of the ladder 3.0 meters from the wall. The coefficient of static friction between the floor and the ladder is 0.28. What distance (d), measured along the ladder from the bottom, can a 60.0 kg person climb before the ladder starts to slip? Hint: the center of gravity of the latter is at its geometry center. Show all work including but not limited to coordinate system, equations along the axis, free body diagrams and torque diagrams. u = 0.28

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter14: Static Equilibrium, Elasticity, And Fracture

Section: Chapter Questions

Problem 31PQ: A wooden door 2.1 m high and 0.90 m wide is hung by two hinges 1.8 m apart. The lower hinge is 15 cm...

See similar textbooks

Similar questions

A 2.4 m ladder rests on a vertical wall as shown in the figure. The ladder has 7 rungs and the rungs are spaced 0.30 m apart, and the top and bottom rungs are 0.30 m from their respective ends of the ladder. Surfaces at A and B both have the same coefficient of friction. If a worker weighs 360 N and stands on the middle rung, determine the minimum value of the coefficient of friction so that the ladder does not slide. Neglect the weight of the ladder.
A 10.0-kg monkey climbs a uniform ladder with weight w = 1.09 ✕ 102 N and length L = 3.40 m as shown in the figure below. The ladder rests against the wall at an angle of ? = 60°. The upper and lower ends of the ladder rest on frictionless surfaces, with the lower end fastened to the wall by a horizontal rope that is frayed and that, can support a maximum tension of only 80.0 N.
A 30 ft ladder, weighing 100 lbs having its center of mass one-third of the way up from the bottom, rests against a smooth wall so that it makes an angle of 60° with the ground. If the coefficient of friction between the ground and the ladder is 0.4, how high can a 150-lb man go before the ladder slips?
A person is standing on a section of uniform scaffolding as shown in the figure. The section of scaffolding is L = 1.50 m in length, has a ms = 25.5 kg mass, and is supported by three ropes as shown. Determine the magnitude of the tension in each rope when a person with a weight of Wp = 660 N is a distance d = 0.700 m from the left end.
From the step ladder shown in the figure, sides AC and CE are each 2.44 m long and hinged at point C. Bar BD is a tie-rod 0.762 m long, halfway up. A man weighing 845 N climbs 1.8 m along the ladder. Assuming the floor is frictionless and neglecting the mass of the ladder, find the tension (in N) in the tie-rod.
A uniform plank of length 2.00m and mass 30.0kg is supported by three ropes, as indicated by the blue vectors in figure p8.27. Find the tension in each rope when a 700-N person is d=0.500m from the left end.
As shown in the figure below, a uniform beam is supported by a cable at one end and the force of friction at the other end. The cable makes an angle of ? = 30°, the length of the beam is L = 4.75 m, the coefficient of static friction between the wall and the beam is μs = 0.520, and the weight of the beam is represented by w. Determine the minimum distance x from point A at which an additional weight 2w (twice the weight of the rod) can be hung without causing the rod to slip at point A.X =. m
A uniform beam of length L = 2.2 m and mass M = 33 kg has its lower end fixed to pivot at a point P on the floor, making an angle θ = 15° as shown in the digram. A horizontal cable is attached at its upper end B to a point A on a wall. A box of the same mass M as the beam is suspended from a rope that is attached to the beam one-fourth L from its upper end.What is the y-component Py of the force, in newtons, exerted by the pivot on the beam? Py = Write an expression for the tension T in the horizontal cable AB. T = What is the x-component Px of the force, in newtons, exerted by the pivot on the beam? Px =
As shown in the figure below, a uniform beam is supported by a cable at one end and the force of friction at the other end. The cable makes an angle of ? = 30°,the length of the beam is L = 2.75 m,the coefficient of static friction between the wall and the beam is ?s = 0.460, and the weight of the beam is represented by w. Determine the minimum distance x from point A at which an additional weight 2w (twice the weight of the rod) can be hung without causing the rod to slip at point A.x = _________m
An object that weighs 1180 N rests on a lever at a point 0.390 m from a support. On the same side of the support, at a distance of 3.00 m from it, an upward force with magnitude F is applied. Ignore the weight of the board itself. If the system is in equilibrium, what is F? Express your answer in Newtons. where P = 1180 and x = 0.390. _____N
A stepladder of negligible weight is constructed as shown in Figure P10.73, with AC = BC = = 4.00 m. A painter of mass m = 70.0 kg stands on the ladder d = 3.00 m from the bottom. Assuming the floor is frictionless, find (a) the tension in the horizontal bar DE connecting the two halves of the ladder, (b) the normal forces at A and B, and (c) the components of the reaction force at the single hinge C that the left half of the ladder exerts on the right half. Suggestion: Treat the ladder as a single object, but also treat each half of the ladder separately.
What three factors affect the torque created by a force relative to a specific pivot point?