a = -F/m = -147 / 100 = -1.47 m/s^2We now use equation of motion v^2 = u^2 + 2ass =?? u = 85.9 a = -1.47 v = 0so we get 0 = 85.......
We can compute force due to friction as coefficient of friction * force perpendicular to plane
=> 980 * 0.15 = 147N
Acceleration on body, a = -F/m = -147 / 100 = -1.47 m/s^2
We now use equation of motion v^2 = u^2 + 2as
s =?? u = 85.9 a = -1.47 v = 0
so we get
0 = 85.9^2 + 2(-1.47)s
=> 2.94s = 7380
=> s = 2510 m
Determine the acceleration on both sections. Use the a with the distances to determine difference in velocity on 1st segment, then 2nd. First resolve the weight into normal and parallel to ramp vectors. Determine friction force, then F=ma. Ignore dots, which are for formatting only. .............................. Weight . F|| Ramp . Normal . Fƒ Friction ... Accel Angle . µ .... Mass . W=mg .. W∙cosθ .. W∙sinθ ..... µ·FN ... a = (F||-Fƒ) / m [°] ................. [kg] ..... [N] .......... [N] .......... [N] ........... [N] ......... [m/s²] 30 ... 0.05 ... 100 ... 980.7 ... 849.311 ... 490.35 ... 24.5175 ... 4.658 20 ... 0.05 ... 100 ... 980.7 ... 921.556 ... 335.42 ... 16.7710 ... 3.186 Then, apply V² = v² + 2a(S-s) ; V=final velocity, v=initial velocity, S=final displacement, s=initial displacement, a=acceleration v_initial .. S_final .. s_initial ... acceleration ... V_final v ................ S ........... s................. a .................. V [m/s] ........ [m] ......... [m] ............. [m/s²] ............ [m/s] 0 ............. 500 ......... 0 ............ 4.6583 .......... 68.252 68.252 .... 500 ......... 0 ............ 3.1865 .......... 88.571 88.571 .... ??? ......... 0 ........... -1.4711 ............ 0 Use same formula, a=-0.15g, and D = 2666.397m
