# A roller coaster of mass 80.0 kg is moving with a speed of 20.0 m/s at position A as shown in the figure. ?

The vertical height above ground level at position A is 200 m. Neglect friction

(a) What is the total mechanical energy of the roller coaster at point A?

(b) What is the total mechanical energy of the roller coaster at point B?

(c) What is the speed of the roller coaster at point B?

(d) What is the speed of the roller coaster at point C? Relevance
• (a)Total mechanical energy at point A = PE at A + KE at A = mgh + ½mv² = 80.0*9.8*200 + ½*80.0*20.0² = 172,800 J

(b) Total mechanical energy at point B = Total mechanical energy at point A = 172,800 J

(c) Total mechanical energy at point B = PE at B + KE at B

172,800 = 0 + ½mv²

v² = 2*172,800/m

v = √(2*172,800/m)

v = √(2*172,800/80.0)

v = 65.7 m/s

speed of roller coaster at point B is 65.7 m/s

(d) Total mechanical energy at point D = Total mechanical energy at point A

PE at C + KE at CA = 172,800

mgh + ½mv² = 172,800

½mv² = 172800 - mgh

v² = 2(172800 - mgh)/m

v = √[2(172800 - mgh)/m]

v = √[2(172800 - 80.0*9.8*160)/80.0]

v = 34.4 m/s

Speed at point C is 34.4 m/s