Question

You are riding the Rollicking Roller Coaster.    At the carts current position, it has a height of 50 m and a speed of 12 m/s. At the first dip the height has reduced to 10 m. Assuming the cart has a mass of 100 kg. What is:

a) The initial gravitational potential energy of the cart?

b) The initial kinetic energy of the cart?

c) The total energy of the cart?

d) The gravitational potential energy at the first dip?

e) The kinetic energy at the first dip?

f) The speed of the cart at the first dip?

Answer 1

a) P.E._i = mgh = 100 x 9.8 x50 = 49000 J

b) K.E._i = 0.5mv² = 0.5 x 100 x 12² = 7200 J

c) T.E. = P.E. + K.E. = 56200 J

d) P.E._f = mgh' ₌ 100 x 9.8 x 10 = 9800 J

e) energy conservation

K.E. = T.E. - P.E._f = 46400 J

f) 46400 = 0.5mV_f²

V_f = 30.46 m/s