A uniform ladder with mass m2 = 14kg and length L = 3.2m rests against a smooth wall. A do-it-yourself enthusiastof mass mi = 70kg stands on the ladder a distance d=1.2m from the bottom (measured along the ladder.) There isno friction between the wall and the ladder, but there is a frictional force, with µ. = 0.25, between the floor and theladder. Nj is the magnitude of the normal force exerted by the wall on the ladder, and Nz is the magnitude of thenormal force exerted by the ground on the ladder.What angle 0, will cause the static friction with the floor to be maximized? Will the ladder start to slip when theangle is made larger, or smaller than this borderline value?1) Draw a free body diagram for the ladder, choose a coordinate system and write out the equations forthe sum of the x forces and the sum of the y forces.2) Draw a diagram of the ladder with each force vector acting on it at its point of application. Chose anaxis of rotation and place this on the diagram as well. (Note: Any choice will work, you just have to beconsistent later.)3) Find the length of the lever arm for each force acting on the ladder, and also list whether that forcewould tend to cause clockwise or counter-clockwise rotation.4) Write out the net torque equation for the ladder.5) Setting the static friction to maximum, use algebra to solve the pair of equations in 1 and 4 for theangle of the ladder.

Answered: Image /qna-images/answer/783ae9f7-eca4-4867-b4d9-ea7db9155618.jpg

A uniform ladder with mass m; = 14kg and length L= 3.2m rests against a smooth wall. A do-it-yourself enthusiast of mass m = 70kg stands on the ladder a distance d= 1.2m from the bottom (measured along the ladder.) There is no frietion between the wall and the ladder, but there is a frictional force, with µ. = 0.25, between the floor and the ladder. Nj is the magnitude of the normal force exerted by the wall on the ladder, and N; is the magnitude of the normal force exerted by the ground on the ladder. What angle e, will cause the static friction with the floor to be maximized? Will the ladder start to slip when the angle is made larger, or smaller than this borderline value?

A uniform ladder with mass m; = 14kg and length L= 3.2m rests against a smooth wall. A do-it-yourself enthusiast of mass m = 70kg stands on the ladder a distance d= 1.2m from the bottom (measured along the ladder.) There is no frietion between the wall and the ladder, but there is a frictional force, with µ. = 0.25, between the floor and the ladder. Nj is the magnitude of the normal force exerted by the wall on the ladder, and N; is the magnitude of the normal force exerted by the ground on the ladder. What angle e, will cause the static friction with the floor to be maximized? Will the ladder start to slip when the angle is made larger, or smaller than this borderline value?

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Similar questions

Two uniform planks, each of mass m = 7.45 kg and length L = 2.51 m, are connected by a hinge at the top and by a chain of negligible mass attached at their centers, as shown in the figure. The assembly will stand upright, in the shape of an A, on a frictionless surface without collapsing. If the chain has the length 0.81 m, find each of the following:a) the absolute value of the tension in the chain,b) the absolute magnitude of the force on the hinge of each plank,
The drawing shows an A-shaped ladder. Both sides of the ladder are equal in length. This ladder is standing on a frictionless horizontal surface, and only the crossbar (which has a negligible mass) of the " A " keeps the ladder from collapsing. The ladder is uniform and has a mass of 15.2Kg. Det k mine the tension in the crossbar of the ladder.
F y mg f.Y Frxe f,x Axis The ladder in the picture has a mass of 32 kilograms and a length 3.2 meters. What is the normal force pushing the ladder up from the floor? FN = Assume that the ladder's weight is evenly distributed, so it can be treated as a single force through the middle. If the ladder is at a 60° angle from the ground, what is the torque exerted by the weight (using the floor as the pivot point)?
A L=4 m long ladder with mass m=10 kg is leaning against a frictionless wall and on a floor with a friction coefficient of 0.5. The ladder's center of mass is in the middle of the ladder. Calculate the largest opening angle between the ladder and the frictionless wall for which a person of mass 75 kg can climb all the way up the ladder without it slipping.
A painter leans a ladder against a wall at an angle of 60˚ to the ground. (Assume the ladder is uniform and the center of mass of the ladder is located at the middle of the ladder.) The ladder is 3.00m long and has a mass of 10.0kg. The person has a mass of 90.0kg. How far up the ladder can the painter climb before it slips if the coefficient of friction is 0.45?
A 420-N uniform rectangular sign 4.00 m wide and 3.00 m high is suspended from a horizontal, 6.00-m-long, uniform, 130-N rod as indicated in the figure below. The left end of the rod is supported by a hinge and the right end is supported by a thin cable making a 30.0° angle with the vertical. (Assume the cable is connected to the very end of the 6.00-m-long rod, and that there are 2.00 m separating the wall from the sign.) 30.0 IE CEAM MOP (a) Find the (magnitude of the) tension T in the cable. N (b) Find the horizontal and vertical components of the force exerted on the left end the rod by the hinge. (Take up and to the right to be the positive directions. Indicate the direction with the sign of your answer.) horizontal component vertical component
A 2.0 m long, 200 N uniform ladder, rests with one end against a smooth wall making an angle of 30° with the wall. The coefficient of static friction between the ground and the lower end of the ladder is 0.5. A force F pushes the upper end of the ladder parallel to the wall so that the ladder is on the verge of starting to slip down (static friction has reached its maximum value). The torque of the weight of the ladder relative to the lower end in the ground is: a. 200 Nm b. 620 Nm C. 546 Nm d. 400 Nm e. None of the above I
A ladder of mass M and length L 4 m is on a level floor leaning againsta vertical wall. The coefficient static friction between the ladder and floor is mus = .6. while the friction between the ladder and the wall is negligible. The ladder is at an angle of 50 degrees above the horizontal. A man of mass 3M starts to climb the ladder. To what distance up the ladder can the man climb before the ladder starts to slip on the floor? Question 11.59 x = 0.8 O.3 0.6 0.5 O.2
A 560-N uniform rectangular sign 4.00 m wide and 3.00 m high is suspended from a horizontal, 6.00-m-long, uniform, 150-N rod as indicated in the figure below. The left end of the rod is supported by a hinge and the right end is supported by a thin cable making a 30.0° angle with the vertical. (Assume the cable is connected to the very end of the 6.00-m-long rod, and that there are 2.00 m separating the wall from the sign.) T 30.0 ICE CREAM SHOP (a) Find the (magnitude of the) tension T in the cable. (b) Find the horizontal and vertical components of the force exerted on the left end of the rod by the hinge. (Take up and to the right to be the positive directions. Indicate the direction with the sign of your answer.) horizontal component vertical component N
Two uniform planks, each of mass m = 7.45 kg and length L = 2.51 m, are connected by a hinge at the top and by a chain of negligible mass attached at their centers, as shown in the figure. The assembly will stand upright, in the shape of an A, on a frictionless surface without collapsing. If the chain has the length 0.81 m, find each of the following: a) the absolute value of the tension in the chain, b) the absolute magnitude of the force on the hinge of each p lank