A solide (S), of m=100g, is launched from the point O to moves up on an inclined plane by an angle a-30 with the horizontal. The motion of (S) is represented by the motion of its center of mass G on ox where i is a unit vector along this axis. At to-0, the speed of (S) is v=5i (m/s). The horizontale plane passing through O is taken as a gravitational potentiel energy reference. A- Frictional forces are negligible: 1. 1.1 The mechanical energy of the system (S-Earth) is conserved. Why? 1.2 Calculate the value of the ME at to-0. 2. After a certain time (S) is on M, such as OM-x, and its speed is v Determine in terms of x: 2.1 The expression of Gpe (the gravitational potentiel energy). 2.2 The expression of KE (kinetic energy). 2.3 Determine the position M, where the kinetic energy and the gravitational energy are equal. OH X E(7) 1,25 1 0,35 10.45- 0,5 0,25 (/) Doc 1 3. The curves of Doc.1, represent the variation of two types of energies during the motion of (S): 3.1 Identify the two curves. 3.2 Using the graph, Refind and determine the position XM of M, where the kinetic energy is equal to the gravitational potentiel energy. 3.3 Using the graph, determine the value of Gpe for X= 2m, Deduce the KE and the speed in this position. 3.4 (S) reaches a maximum position Xm, when it turns back. Determine Xm. 1. Determine the ME for x=2m (Notice that the solide S stop in this position). 2. Calculate AME (the variation of the ME). 3. Deduce the value of f. 1.15 2 25 3 ) B-In reality, the frictional forces are not negligible, are assumed constant and value of f: