Answer:
(a) The car is going approximately 40.43 m/s at the bottom of the hill
(b) The thermal energy will increase by 607,268.76 J
Explanation:
In the question, we have;
The height of the roller coaster above ground = 83.4 m
The mass of the roller coaster, m = 743.0 kg
(a) By the conservation of energy principle, we have;
The potential energy at the top of the hill, P.E., is equal to the kinetic energy at the bottom of the hill, K.E.
∴ P.E. = K.E.
P.E. = m·g·h
Where;
m = The mass of the roller coaster = 743.0 kg
g = The acceleration due to gravity = 9.8 m/s²
h = The height of the roller coaster = 83.4 m
Therefore, we have;
P.E. = 743.0 kg × 9.8 m/s² × 83.4 m = 607,268.76 J
P.E. = 607,268.76 J
K.E. = 1/2·m·v²
∴ K.E. = 1/2 × 743.0 kg × v²
P.E. = K.E.
∴ P.E. = K.E. = 607,268.76 J
1/2 × 743.0 kg × v² = 607,268.76 J
v² = 607,268.76 J/(1/2 × 743.0 kg) = 1,634.64 m²/s²
v = √(1,634.64 m²/s²) ≈ 40.43 m/s
(b) Given that the material wheel moves along polystyrene track, the sound released will be minimal and almost all the kinetic energy will be converted to heat energy when the train stops, therefore, the thermal energy will increase by K.E. = 607,268.76 J
