Concept explainers
You’re investigating ladder safety for the Consumer Product Safety Commission. Your test case is a uniform ladder of mass m leaning against a frictionless vertical wall with which it makes an angle θ. The coefficient of static friction at the floor is μ. Your job is to find an expression for the maximum mass of a person who can climb to the top of the ladder without its slipping. With that result, you’re to show that anyone can climb to the top if μ ≥ tan θ land but that no one can if
Want to see the full answer?
Check out a sample textbook solutionChapter 12 Solutions
Essential University Physics (3rd Edition)
Additional Science Textbook Solutions
College Physics: A Strategic Approach (4th Edition)
College Physics
Essential University Physics: Volume 1 (3rd Edition)
Sears And Zemansky's University Physics With Modern Physics
College Physics: A Strategic Approach (3rd Edition)
Conceptual Physics (12th Edition)
- A 3.0 m long ladder leans against a frictionless wall at an angle of 60°. What is the minimum value of the coefficient of static friction that prevents the ladder from slipping?arrow_forwardA 15 kg monkey climbs a uniform ladder with weight 1.2 *10^2 N and length L=3.00 m. The ladder rests against the wall and makes an angle of theta= 60.0 degrees with the ground. The upper and lower ends of the ladder rest on frictionless surfaces. The lower end is connected to the wall by a horizontal rope. HInt : Draw a force diagram for the ladder and the normal forces from the ground and wall acting on the ladder. A) find the tension in the rope when the monkey is two-thirds of the way up the ladder. B) The rope is frayed and can support a maximum tension of only 80N. Find the maximum distance that the monkey can climb up the ladder before the rope breaks. C) If the horizontal surface were rough and the rope were removed, how would your analysis of the problem change? What other information would you need to answer parts (a) and (b)arrow_forwardA 10.0-kg monkey climbs a uniform ladder with weight 1.20 × 102 N andlength L = 3.00 m as shown. The ladder rests against the wall and makes an angle of θ = 60.0° with the ground. The upper and lower ends of the ladder rest on frictionless surfaces. The lower end is connected to the wall by a horizontal rope that is frayed and can support a maximum tension of only 80.0 N. (a) Draw a force diagram for the ladder. (b) Find the normal force exerted on the bottom of the ladder. (c) Find the tension in the rope when the monkey is two-thirds of the way up the ladder. (d) Find the maximum distance d that the monkey can climb up the ladder before the rope breaks. (e) If the horizontal surface were rough and the rope were removed, how would your analysis of the problem change? What other information would you need to answer parts (c) and (d)?arrow_forward
- It's exciting watching the construction and renovation happening in Uptown Columbus! On one construction site, you notice that a uniform beam of length 13.6 m and mass 47.9 kg is attached to a wall by a cable. The angle between the cable and the beam is 59.5°. The beam is free to pivot about the point where it attaches to the wall. What is the tension in the cable, if the beam is not moving? Your Answer: Answerarrow_forwardA uniform ladder 5.0 m long rests against a frictionless, vertical wall with its lower end 3.0 m from the wall. The ladder weighs 160 N. The coefficient of static friction between the foot of the ladder and the ground is 0.40. A man weighing 740 N climbs slowly up the ladder. (a) What is the maximum friction force, in Newtons, that the ground can exert on the ladder at its lower end? (b) What is the actual friction force, in Newtons, when the man has climbed 1.0 m along the ladder? (c) How far, in meters, along the ladder can the man climb before the ladder starts to slip?arrow_forwardA uniform ladder of mass mmm and length lll leans at an angle θθtheta against a frictionless wall (Figure 1).If the coefficient of static friction between the ladder and the ground is μμmu, determine a formula for the minimum angle at which the ladder will not slip. Express your answer in terms of some or all of the variables mmm, lll, and μμmu.arrow_forward
- A 3.0-m-long ladder leans against a wall at an angle of 60° with respect to the floor. What is the minimum value of μs , the coefficient of static friction with the ground, that will prevent the ladder from slipping? Assume that friction between the ladder and the wall is negligible.arrow_forwardHelp me pleasearrow_forwardIf each cable can withstand a maximum tension of 1000 N, determine the largest mass o the cylinder for equilibrium. Solution: m = 90.3 kg B C 3 m 2 m 2 m 1 m 1m A 3 m D 4 m 1.5 marrow_forward
- A 100-N uniform ladder, 8.0 m long, rests against a smooth vertical wall. The coefficient of static friction between ladder and floor is 0.40. What minimum angle can the ladder make with the floor before it slips?arrow_forwardIn the figure, a 87 kg sphere is supported on a frictionless plane inclined at angle 0 = 48° from the horizontal. Angle o is 28°. Calculate the tension in the cable. Cable Number Unitsarrow_forwardA uniform ladder of length L and weight w is leaning against a vertical wall. The coefficient of static friction between the ladder and the floor is the same as that between the ladder and the wall. If this coefficient of static friction is µ = 0.385, determine the smallest angle the ladder can make with the floor without slipping.arrow_forward
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning