Answer to Question #287078 in Classical Mechanics for elle

Question

the loaded roller coaster has a mass of 2500 kg. the starting point of the run is 22m above point A; the run from B to C is 120m long; the run from C to D is 100m. at D, brakes are applied, bringing the coaster to a halt 15m further along a E. if the friction from B to D is 0, find

(a) the potential energy of the roller coaster at the starting point

(b) KE of the roller coaster at C

(c) the speed of the roller coaster at D; the average braking force applied between D and E

Answer 1

a)

$E_A=mgh_A=0.55~MJ,$

b)

$K_C=E_A-E_C=mg(h_A-h_C)=0.18~MJ,$

c)

$v_D=\sqrt{\frac{2E_D}m}=\sqrt{\frac{2mg(h_A-h_D)}m}=\sqrt{2g(h_A-h_D)}=11.8~\frac ms,$

d)

$Fl_{DE}=E_D=mg(h_A-h_D),$

$F=\frac{mg(h_A-h_D)}{l_{DE}}=23.3~kN.$