A stepladder of negligible weight is constructed as shown 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.)
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- In the figure below, a uniform beam of weight 420 N and length 2.8 m is suspended horizontally. On the left it is hinged to a wall; on the right is it supported by a cable bolted to the wall at distance D above the beam. The least tension that will snap the cable is 1200 N. Cable Beam (a) What value of D corresponds to that tension? (b) Give any value for D that won't snap the cable. mThe drawing shows a uniform horizontal beam attached to a vertical wall by a frictionless hinge and supported from below at an angle 0 = 40° by a brace that is attached to a pin. The beam has a weight of 340 N. Three additional forces keep the beam in equilibrium. The brace applies a force P, and the hinge applies a force with a horizontal component H and a vertical component V. (a) Draw the free- body diagram showing the forces that act on the beam. Find the magnitudes of the forces (b) P, (c) H, and (d) V. Beam Hinge Pin Ꮎ Brace EA 355 N uniform ladder of length L= 8.00 m leans against a smooth (frictionless) wal The ladder mnakes an angle of 50.0° angle with the horizontal ground and the force of static friction keeps the ladder from sliding to the left. An 875 N firefighter has climbed d = 6.30 m along the ladder trom the bottom. What is the force of static friction f, between the ladder and the ground? 50.0 O 119 N O 480 N O 727 N O 567 N command eptien
- A 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?Ea- d ms A horizontal L=1.4 m long mb3D12kg uniform bar is hinged on the left end and pulled at the right end by a cable. The cable makes 30° angle with horizontal. A 22 kg store sign is suspended below the bar at d=0.18 m from the right end. Find the magnitude of horizontal hinge force.A uniform 34.0-kg beam of length { = 5.95 m is supported by a vertical rope located d = 1.20 m from its left end as in the figure below. The right end of the beam is supported by a vertical column. (a) Find the tension in the rope. (b) Find the force that the column exerts on the right end of the beam. (Enter the magnitude.)
- One end of a uniform 4.10-m-long rod of weight Fg is supported by a cable at an angle of ? = 37° with the rod. The other end rests against the wall, where it is held by friction as shown in the figure below. The coefficient of static friction between the wall and the rod is ?s = 0.480. Determine the minimum distance x from point A at which an additional object, also with the same weight Fg, can be hung without causing the rod to slip at point A. ------mProblem 6: A uniform stationary ladder of length L and mass M leans against a smooth vertical wall, while its bottom legs rest on a rough horizontal floor. The coefficient of static friction between floor and ladder is u. The ladder makes an angle with respect to the floor. A painter of weight 1/2M stands on the ladder a distance d from its base. What is the largest value for d, in centimeters, such that the ladder will not slip? Assume that ladder is 5.5 m long, the coefficient of friction is 0.51, the ladder is at an angle of 48°, and the ladder has a mass of 75 kg. dmax = sin() cos() tan() JT ( 7 8 9 HOMEOne end of a uniform { = 4.30-m-long rod of weight w is supported by a cable at an angle of 0 = 37° with the rod. The other end rests against a wall, where it is held by friction (see figure). The coefficient of static friction between the wall and the rod is µ. = 0.490. Determine the minimum distance x from point A at which an additional weight w (the same as the weight of the rod) can be hung without causing the rod to slip at point A. B Need Help? Read It Watch It
- A block with a mass of m = 1.5 kg rests on a wooden plank. The coefficient of static friction between the block and the plank is μs = 0.44. One end of the board is attached to a hinge so that the other end can be lifted forming an angle, θ, with respect to the ground. Assume the x-axis is along the plank as shown in the figure. a)Assuming the x-direction is along the plank as shown, find an expression for the magnitude of the force of gravity in the y-direction, Fgy, perpendicular to the plank in terms of given quantities and variables available in the palette. b)Write an expression for the magnitude of the maximum friction force along the surface, Fs, in terms of given quantities and variables available in the palette. c)Assuming the static friction is maximized, write an expression, using only the given parameters and variables available in the palette, for the sum of the forces along the plank, ΣFx.A ladder rests against a frictionless wall. It has a mass of 40 kg, a length of 6.4 m, and makes an angle of 56° with the ground. Find the horizontal and vertical force components exerted by the ground on the bottom of the ladder if a standard man stands on the ladder 4 m from the ground. (Assume the mass of the standard man is 70 kg. Enter the magnitudes in newtons.)