In the figure, a ladder of length L = 11 m and mass m = 48 kg leans against a slick (frictionless) wall. The ladder's upper end is at height h = 8.3 m above the pavement on which the lower end rests(the pavement is not frictionless). The ladder's center of mass is L/3 from the lower end. A firefighter of mass M = 71 kg climbs the ladder. Let the coefficient of static friction us between the ladderand the pavement be 0.46. How far (in percent) up the ladder must the firefighter go to put the ladder on the verge of sliding?FrictionlessSystemFire-Fire-/fighterfightercomLadderLaddercoma/3a/2-

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Answered: In the figure, a ladder of length L =…

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 82PQ

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A stepladder of negligible weight is constructed as shown in Figure P10.73, with AC = BC = ℓ. A painter of mass m stands on the ladder a distance d 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. Figure P10.73 Problems 73 and 74.
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.
A uniform beam resting on two pivots has a length L = 6.00 m and mass M = 90.0 kg. The pivot under the left end exerts a normal force n1 on the beam, and the second pivot located a distance = 4.00 m from the left end exerts a normal force n2. A woman of mass m = 55.0 kg steps onto the left end of the beam and begins walking to the right as in Figure P10.28. The goal is to find the womans position when the beam begins to tip. (a) What is the appropriate analysis model for the beam before it begins to tip? (b) Sketch a force diagram for the beam, labeling the gravitational and normal forces acting on the beam and placing the woman a distance x to the right of the first pivot, which is the origin. (c) Where is the woman when the normal force n1 is the greatest? (d) What is n1 when the beam is about to tip? (e) Use Equation 10.27 to find the value of n2 when the beam is about to tip. (f) Using the result of part (d) and Equation 10.28, with torques computed around the second pivot, find the womans position x when the beam is about to tip. (g) Check the answer to part (e) by computing torques around the first pivot point. Figure P10.28
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 above the bottom of the door. The center of mass of the door is at its geometric center, and the weight of the door is 260 N, which is supported equally by both hinges. Find the horizontal force exerted by each hinge on the door.
In Figure P10.40, the hanging object has a mass of m1 = 0.420 kg; the sliding block has a mass of m2 = 0.850 kg; and the pulley is a hollow cylinder with a mass of M = 0.350 kg, an inner radius of R1 = 0.020 0 m, and an outer radius of R2 = 0.030 0 m. Assume the mass of the spokes is negligible. The coefficient of kinetic friction between the block and the horizontal surface is k = 0.250. The pulley turns without friction on its axle. The light cord does not stretch and does not slip on the pulley. The block has a velocity of vi = 0.820 m/s toward the pulley when it passes a reference point on the table. (a) Use energy methods to predict its speed after it has moved to a second point, 0.700 m away. (b) Find the angular speed of the pulley at the same moment. Figure P10.40
Why is the following situation impossible? A uniform beam of mass mb = 3.00 kg and length ℓ = 1.00 m supports blocks with masses m1 = 5.00 kg and m2 = 15.0 kg at two positions as shown. The beam rests on two triangular blocks, with point P a distance d = 0.300 m to the right of the center of gravity of the beam. The position of the object of mass m2 is adjusted along the length of the beam until the normal force on the beam at O is zero.
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 =
A uniform plank of length 5.0 m and weight 225 N rests horizontally on two supports, with 1.1m of the plank hanging over the right support. To what distance x can a person who weighs 377 N walk on the overhanging part of the plank before it just begins to tip?
Consider a see-saw of total length 5.40m balanced at its center of mass, with a child of mass 35.00kg sitting on the left-most edge. If a second child of mass 46.00kg wants to balance the see-saw, what distance from the pivot point must the second child sit? ____m
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 teeter totter is made of a uniform plank of mass 20 kg and length 8 m. A girl of mass 30 kg is positioned at one end and a boy of mass 45 kg is positioned at the opposite end. How far from the girl is the fulcrum of the teeter totter located when it is in balance? a. 3.37 m b. 4.00 m c. 4.63 m d. 5.50 m e. 7.99 m
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

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