# Statics Of Rigid Bodies Pdf

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Section 2.3 Solid Mechanics Part I Kelly 19 2.3 The Statics of Rigid Bodies. Rigid Bodies Equivalent Force/Moment Systems. 2 MEM202 Engineering Mechanics - Statics MEM Equilibrium of Rigid Bodies.

10 Problems in Statics of Rigid Bodies Consider the wedge used to lower and raise block A The vertical position of a machine (block A) is adjusted by moving wedge B. The coefficient of static friction between all surfaces is 0.3. Determine the horizontal force, P, acting on wedge B, that is required to a) raise the block A (acting on the right side) The first part of this problem asks for the the smallest value of the force, P, to raise the machine. This force will act on the right side of the wide of block A, as shown, in order to push block A upward.

As with all static problems, a free-body diagram will help identify all forces acting on an object. Free body diagram Since there is a known force of 1,500 lb acting on block A, this object will be analyzed first. All forces acting on the block 'A' are shown in the free-body diagram on the left.

## Rigid Bodies

The frictional forces are, f1 = μ N1 = 0.3 N1 f2 = μ N2 = 0.3 N2 Applying the equilibrium equations gives, ΣFx = 0 N1 - f2 cos 12 - N2 sin 12 = 0 N1 - (0.3) (0.9781) N2 - 0.2079 N2 = 0 N1 = 0.5013 N2 ΣFy = 0 N2 cos 12 - f1 - 1,500 - f 2 sin 12 = 0 0.9781 N2 - 0.3 N1 - 1,500 - (0.3)(0.2079) N2 = 0 0.9158 N2 - 0.3 N1 = 1,500 Solving above two equations gives, N2 = 1,960 lb N1 = 982.4 lb and the frictional forces are, f2 = 587.9 lb f1 = 294.7 lb Now that the forces on the bottom surface of block A are known,wedge B can be analyzed. First, sum the forces in the vertical direction, to give, ΣFy = 0 N3 + f2 sin 12 - N2 cos 12 = 0 N3 + (587.9) (0.2079) - (1,960) (0.9781) = 0 N3 = 1,795 lb and f3 = 538.5 lb Finally, P can be determined by summing forces on wedge B in the horizontal, Fx = 0 N2 sin 12 + f3 + f2 cos 12 - P = 0 (1,960) (0.2079) + 538.5 + (587.9) (0.9781) = P P = 1,521 lb Problem 2 Problem 1 Two sleds are tied together with a rope (Figure 3). The coefficient of static friction between each sled and the snow is 0.22. A small child is sitting on sled 1 (total mass of 27 kg) and a larger child sits on sled 2 (total mass of 38 kg).

An adult pulls on the sleds. (a) What is the greatest horizontal force that the adult can exert on sled 1 without moving either sled? Solution (a) The two sleds do not move when the adult pulls on sled 1. This means that the net force acting on the sleds is zero and the applied force must be cancelled by the total maximum force of static friction acting on the two sleds. To calculate the static friction, we combine the two masses and treat the sleds as one single object. Given: m=27 kg + 38 kg= 65 kg; u=0.22 If the force of F = 100 lb is applied to the handle of the bar bender. Determine the horizontal and vertical components of reaction at pin A and the reaction of the roller B on the smooth bar.

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Problem 3 The jib crane is supported by a pin at C and rod AB. If the load has a mass of 2 Mg with its center of mass located at G, determine the horizontal and vertical components of reaction at the pin C and the force developed in rod AB on the crane when x = 5 m. Problem 4 Determine the horizontal and vertical components of reaction at the pin A and the normal force at the smooth peg B on the member Problem 5 Spring CD remains in the horizontal position at all times due to the roller at D.  If the spring is unstretched when angle is= 0 degrees and the bracket achieves its equilibrium position when the angle is= 30 degrees, determine the stiffness k of the spring and the horizontal and vertical components of reaction at pin A. Problem 6 Determine the horizontal and vertical components of reaction at the pin A and the reaction of the smooth collar B on the rod Problem 7 Determine the horizontal and vertical components of force at the pin A and the reaction at the rocker B of the curved beam. Problem 8 The floor crane and the driver have a total weight of 2500 lb with a center of gravity at G. If the crane is required to lift the 500-lb drum, determine the normal reaction on both the wheels at A and both the wheels at B when the boom is in the position shown. Problem 9 Determine the magnitude of force F that must be exerted on the handle at C to hold the 75-kg crate in the position shown. Also, determine the components of reaction at the thrust bearing A and smooth journal bearing B. Problem 10 by: Christine Baterbonia Maurice Ancanan Jennalyn Castro Marie Kirsty Onia:). 