Download Engineering Mechanics-Dynamics Kinetics of Particles: Work and Energy and more Schemes and Mind Maps Engineering in PDF only on Docsity! Engineering Mechanics-Dynamics Kinetics of Particles: Work and Energy 32 Asst. Prof. Dr. Sheelan M. Hama Chapter TWO Kinetics of Particles: Work And Energy 2-9 The Work of a Force A force F will do work on a particle only when the particle undergoes a displacement in the direction of the force. For example, if the force F in Fig. causes the particle to move along the path s from position r to a new position r', the displacement is then dr = r' - r. The magnitude of dr is ds, the length of the differential segment along the path. If the angle between the tails of dr and F is θ, then the work done by F is a scalar quantity, defined by dU = F ds cos θ By definition of the dot product this equation can also be written as dU = F . dr 2-9-1 Work of a Variable Force If the particle acted upon by the force F undergoes a finite displacement along its path from r1 to r2 or s1 to s2 , the work of force F is determined by integration. Provided F and θ can be expressed as a function of position, then Engineering Mechanics-Dynamics Kinetics of Particles: Work and Energy 33 Asst. Prof. Dr. Sheelan M. Hama Constant Force Moving Along a Straight Line Work of a 2-9-2 If the force Fc has a constant magnitude and acts at a constant angle θ from its straight-line path, then the component of Fc in the direction of displacement is always Fc cos θ. The work done by Fc when the particle is displaced from s1 to s2 is determined from, in which case Here the work of Fc represents the area of the rectangle as in Figure below: 2-9-3 Work of a Weight Consider a particle of weight W, which moves up along the path s shown in Fig. from position s1 to position s2 . Engineering Mechanics-Dynamics Kinetics of Particles: Work and Energy 36 Asst. Prof. Dr. Sheelan M. Hama If we apply the principle of work and energy to this and each of the other particles in the system, then since work and energy are scalar quantities, the equations can be summed algebraically, which gives Problems involve cases where a body slides over the surface of another body in the presence of friction considers as special class of problems which requires a careful application. Consider, for example, a block which is translating a distance s over a rough surface as shown in Fig. If the applied force P just balances the resultant frictional force µk N. Engineering Mechanics-Dynamics Kinetics of Particles: Work and Energy 37 Asst. Prof. Dr. Sheelan M. Hama Example 10: The 3500-lb automobile shown in Fig. travels down the 10° inclined road at a speed of 20 ft/s. If the driver jams on the brakes, causing his wheels to lock, determine how far s the tires skid on the road. The coefficient of kinetic friction between the wheels and the road is µk = 0.5. SOLUTION:
