To get up on the roof, a person (mass 66.7 kg) places an aluminum ladder (mass 9.30 kg) against the house on a concrete pad with the base of the ladder 2.27 m from the house. The ladder rests on a plastic rain gutter, which we can assume to be frictionless. The gutter is 6.96 m from the bottom of the ladder. The center of mass of the ladder is 2.32 m from the bottom. The person is standing 3.32 m from the bottom of the ladder. What are the magnitudes of the forces on the ladder at the top and bottom? At bottom of ladder: normal force = 775 friction force = 106 Magnitude of force on bottom of ladder = 782 N At top of ladder, normal force = 106

A homogeneous, 4-ft-wide, 7.8-ft-long rectangular gate weighing 800 lb is held in place by a horizontal flexible cable as shown in the figure below. Water acts against the gate, which is hinged at point A. Friction in the hinge is negligible. Determine the tension in the cable Assume L: -7.8 ft. L₂-3.8 ft, and 0 = 45% T- Water Cable Gate Hinge Lo

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You are designing a hydraulic lift for an automobile garage. It will consist of two oil-filled cylindrical pipes of different diameters. A worker pushes down on a piston at one end (d = 25cm), raising the car on a platform at the other end (d=?). To handle a full range of jobs, you must be able to lift cars up to 3000 kg, plus the 700 kg platform on which they are parked. To avoid injury to your workers, the maximum amount of force a worker should need to exert is 100 N. What should be the diameter of the pipe under the platform? If the worker pushes down with a stroke 50 cm long, by how much will he raise the car at the other end?

A three wheeled OTV has been designed such that the forces from the wheels and motors are uniform, hence the reaction forces at the point of contact with the upper surface can be modeled as a single vertical reaction support. The platform is a square with side length 200mm and has a thickness of 20mm. Plywood has a density of 0.3 g/cm^3. For the purposes of finding the platform weight, W, ignore any holes in the plywood for motor mounts. Due to a misscommunication in the team, the motor mounts M1, M2, and M3 were not attached symmetrically! The potential consequences of this are a difference in reaction forces at the platform to keep it balanced. This difference in reaction forces will result a different normal force at each wheel, and hence the potential for different traction forces, leading to an inability to drive the OTV straight. Co • F: (-75,-75) F₂: (85, -75) • F3: (15,85) -17.4319 MAT 1.338758 3.18886 7 Top View A coordinate system has been defined, such that middle of the…

Your engineering firm is asked to specify the maximum load for theelevators in a new building. Each elevator has a mass 490 kg when empty and maximumacceleration 2.24 m/s2. The elevator cables can withstand a maximum tension of 19.5 kN beforebreaking. For safety, you need to ensure that the tension never exceeds two-thirds of that value.What is the maximum load that the elevator can safely carry? How many70-kg people is that?Briefly but clearly explain the reasoning for your choice of the sign of the acceleration.

As shown in Figure 2.3, the total height of the liquid in the canal in Part (a) is now increased to 3R. Determine the minimum force F applied at B to prevent the gate ABC from opening (i.e. turning anticlockwise about the hinge A). Neglect the weight of the gate and friction in the hinge. F- 2R Air с B Gate R Air Liquid Hinge Figure 2.3 Р 777. gv