A uniform symmetrical beam is supported at two pin joints as shown below. It has a length L and a uniformly distributed load P: (x) = p is applied. The maximum bending moment M, (x) will be half way along the beam.
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- 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,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)?for the below figure, the rod of mass 50kg and length 6m is in the equilibrium. It is hinged to a wall at 0. The rod is at an angle of 40˚ above the horizontal and the rope makes an angle of 70˚ with the rod. (a)find the tension in the rope (b)find the force exerted by the hinge 0 on the rod.
- The uniform 19.0 kg beam below is 6.4 m long and is perfectly balanced about a point 1.4 m from the left end. What is the mass of the block? (Hint: when calculating the torque due to the weight of the beam, consider all of its mass to be located at its center of mass.)A uniform rod is attached to a wall by a hinge at its base. The rod has mass of 8.0 kg, a length of 1.8 m, is at an angle of 17° above the horizontal, and is held in place by a horizontal cord attached to the other end of the rod and bolted to the wall above the base of the rod. (a) Determine the tension in the cord. N (b) Determine the horizontal and vertical components of the force exerted on the rod by the hinge. FH = N Fv = NStructural member AB is to be supported by a strut CD. Determine the smallest length CD may have, and specify where D must be located for a strut of this length to be used. Take x= 120 mm. 60 mm D. y 20 mm E The smallest length CD may have is mm. The coordinates of point Dare ( and Imm.
- You have been hired to design a family-friendly see-saw. Your design will feature a uniform board (mass M, length L) that can be moved so that the pivot is a distance d from the center of the board. This will allow riders to achieve static equilibrium even if they are of different mass, as most people are. You have decided that each rider will be positioned so that his/her center of mass will be a distance xoffset from the end of the board when seated as shown. You have selected a child of mass m (shown on the right), and an adult of mass n times the mass of the child (shown on the left) to test out your prototype. (a) Derive an expression for the torque applied by the adult rider (on the left) in terms of given quantities and variables available in the palette. Assume counterclockwise is positive. (b) Derive an expression for the torque applied by the child rider (on the right) in terms of given quantities and variables available in the palette. Assume counterclockwise is positive.…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 lankIn an emergency situation, a person with a broken forearm ties a strap from his hand to clip on his shoulder as in the figure below. His 1.60-kg forearm remains in a horizontal position and the strap makes an angle of ? = 47.0° with the horizontal. Assume the forearm is uniform, has a length of ℓ = 0.332 m, assume the biceps muscle is relaxed, and ignore the mass and length of the hand. A person with a broken left forearm faces out of the page. His left forearm is approximately horizontal, and a strap extends from a clip on his right shoulder to a position on his left arm that is a distance ℓ from the elbow. The strap is at an angle ? above the forearm. A force vector R acts up and to the right on the left forearm at a location just left of the elbow. (a) Find the tension in the strap. N(b) Find the components of the reaction force exerted by the humerus on the forearm. (Assume the positive x-direction is to the right and the positive y-direction is upward.) Rx = N Ry= N