A non-uniform rod is horizontal, and has one end at x = 0 and the other end at x = 20 m. In order to keep the rod horizontal, and above the ground, vertical forces Fo = 5 N (at x = 0) and FL = 3 N (at a = 20 m) need to be applied at the ends. What is the weight W of the rod, and what is the x-coordinate of the center of gravity of the rod?
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- The center of gravity of Kelly's outstretched arm is located 21 cm from the axis of rotation in her shoulder. Her arm has a mass of 4.2 kg and is 56 cm long. Assuming the deltoid's force is horizontal, what is the magnitude of the force her deltoid muscle must exert on Kelly's upper arm so she can hold a 6.0 kg mass stationary 15 degree above the horizontal as shown? Her deltoid muscle attaches to her upper arm at a point 18 cm from her shoulder joint. 6 kg 15° 21 cm FdeltiodPage 4 of 4 Torque And Static Equilibrium 4. A 5-m uniform ladder of mass 15 kg is held stationary against a frictionless wall. If the ladder is in a state of impending motion when it makes an angle of 65° with respect to the floor, calculate the force exerted by the wall onto the ladder. Solution and Answer: Since the ladder is uniform, then the center of gravity of the ladder is at its geometric center. We use the first and second conditions for equilibrium in order to tackle this problem. The chosen axis of rotation is at the point where the ladder makes contact with the ground. Let Fwall and f be the forces due to the wall and due to friction, respectively. From the first conditions of equilibrium, we get: force exerted by wall weighe ermal force ction =f+(-Fwatt) = 0 B = n + (-W) = 0 The second condition for equilibrium is: Twall + (-Triction) + Tn + (-Tweight) = 0 The frictional force and the normal force are located at the pivot point. This further simplifies to: Twall +…A ladder is leaning against a vertical wall, and both ends of the ladder are at the point of slipping. The coefficient of friction between the ladder and the horizontal surface is ?1=0.165 and the coefficient of friction between the ladder and the wall is ?2=0.153 . Determine the maximum angle α with the vertical that the ladder can make without falling on the ground.
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