Figure P.5.3a-c. Distributed force systems acting on a beam.

Figure P.5.4. A man performing seated machine rows.

Figure P.5.5. A rod under axial load. The cross-sectional area of the circular rod varies linearly from one end to the other.

a distance of 0.8 m from point B. The length of the rod is 2.2 m. Its radius at B is 0.3 m and at D is 0.2 m. The rod is made of homogeneous material so that its Young's modulus E does not vary with position. Determine the horizontal support forces at B and D. Hint: Let e1 be the unit vector in the direction of P. Equation of motion in the e1 direction dictates that

where B and D are the horizontal support forces at B and D, respectively. They are positive when directed in - e1 direction. The section of the rod that lies between B and force P is in tension and the remaining section is in compression. As the distance between B and D does not change, elongation S1 of BP must be equal to the amount of compression 82 of PD. The length change 8 of a rod under a uniaxial force is given by

where the integration is over the length of the rod, F is the axial force acting on the rod, dx is a small length element along the axis of the rod, A = A (x) is the cross-sectional area, and E is Young's modulus. The parameter 8 is positive when F is tension and negative when F is compression. Show that in this case A (x) = w (0.3 - 0.045 x)2. Furthermore, the constant length condition reduces to the following equation:

B [0/08(0.3 - 0.045x)-2 dx] = (7,000 - B) [0.8/22(0.3 - 0.045x)-2 dx] Answer: B = 5,075 N, D = 1,925 N.

Problem 5.6. Discuss the potential benefit of heel cushion cups in alleviating the heel pain that afflicts many runners.

Getting Started With Dumbbells

Getting Started With Dumbbells

The use of dumbbells gives you a much more comprehensive strengthening effect because the workout engages your stabilizer muscles, in addition to the muscle you may be pin-pointing. Without all of the belts and artificial stabilizers of a machine, you also engage your core muscles, which are your body's natural stabilizers.

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