Question

Problem 1: Looping. The looping of a roller coaster has the radius R. The roller coaster starts at rest in height H over the deepest point of the looping (as shown in the figure). Neglect friction and consider the roller coaster as a mass point of mass m. Q.1) Express the total energy of the body. The reference point for the potential energy is at the center of the loop. Q.2) Find the speed of the body at the top of the loop. Q.3) In order passengers of the roller not to fall from their seats at the highest point of the looping circle how much should be the minimum value of the starting altitude Hmin? Q.4) Find the normal force (N) exerted by the loop on the body at the bottom of the loop for H = H min For numerical calculations assume that g=10m/s?:m = 100kg; H =19,25m; R = 4m

Answer 1

4. Not At botte Enegy at Emmy Ruine Wmg any point N-mg = m R Eresgu at highest point = mg (HR) 320 wsing enthy. Contovation Mg(HR) = mort+m gR sino = 9 (H-R) -- JR sino u= Roshar (it sino? At top o=90 N = mg + mere = mg + mama 279H-R"C1+ aim o)}} waar oslng0 = mg + min $29(H-R CI+ sin(-30)} = mg+2m0 {M} = mg (t+RA) = 100X10 (1 + 2X.10) (DS is = /28{H-R. (1+ringo)} - 120 (H-2B) -QR) =/2010 (19-2+4) 1920 = 14-8/ PERO = 14-81/ - 6000N Nu my met o ( for not falling UVOR /28 (Humin 2R) = rar 2H m 4 R = R Hain - SR=0X410m