Question

Problem 1 (Decomposition of Forces) (25 pts) (a) (8 pts) Consider a fixed ramp of an inclination angle 0. A block of mass m is placed on the top of the ramp. The surface between the block and ramp is assumed to be frictionless. Draw the free-body diagram for the block, and decompose the F=mä equation into the r- and y-component where -direction is along the ramp while y-direction is perpendicular to the ramp. In case of confusion, I'm asking you to setup the equations in terms of relevant forces and quantities of the form m Fr=ma Fy = may Oy Write your equations in terms of m, 0, 9, the magnitude of the normal force N and the magnitude of the acceleration a. (b) (7 pts) Consider the same problem as in part (a), but now decompose the F = mā equation into the x- and y-component where now 2-direction is in the horizontal direction and y-direction is in the vertical direction. Write your equations in terms of m, 0, 9, the magnitude of the normal force N and the magnitude of the acceleration a. т.

Answer 1

masino E Fx = max mg sino =max Tax=gsino , -- x mgcaso 1 Efy zmay N-mgcoso = m(o) IN=mg caso >x N Ā -> a caso E Fxe = max N sino - macoso - 0. ng Efy=may Ncoso - mg = mi-a sino) © from equation of macaso caso sino como - mg = -masing ma (Cost + sino) = mg th a (can? + sino) mg (1: Sin28460829 =1 la = gsinol & N = m Ca siyo keso = mg caso sind apaun as System is in equilibrium sa Efazo - Tz sin 30° - T3 sin 60%20 - T2 = 3 T3 again, Efyao T - Tz ces 30° – Tg cos bo° 70 T-P3 T3 * 17 2 - T3 x 12 20 so, T3 = 1/2 and T2= BIL if this is clear to you! Thanks !! I please like it