How much energy is lost due to friction?

Question

Heights:

Point A=65m, Point B=52 m, Point C=25m

The total mass of the roller coaster is 650 kg.

In real life, some of the energy the roller coaster has at point A will be lost as thermal energy due to friction as it travels through the track. If the speed of the roller coaster at point C is only 19 m/s, calculate the amount of energy that was lost due to friction. 

Answer 1

Hello Janushka! Please see my answer below.

Total energy (TE) of the roller coaster is a combination of kinetic energy (KE) and potential energy (PE)

Equations: TE=KE+PE KE=(1/2)mv² PE=mgh

**In these equations, m=mass, v=velocity, g=acceleration due to gravity (9.81m/s2), h=height

At point A, the roller coaster starts motionless. Because velocity=0, KE=0.

TE_A = KE_A+PE_A = (1/2)mv²+mgh = (1/2)(650)(0)²+(650)(9.81)(65) = 414472.5 J = 414.5kJ (kiloJoules)

At point C, the roller coaster starts has both potential energy and kinetic energy

TE_C = KE_C+PE_C = (1/2)mv²+mgh = (1/2)(650)(19)²+(650)(9.81)(25) = 117325+159412.5 = 276.7 kJ

The difference between the total energy at point A and point C represents the total amount lost due to friction. 414.5 kJ - 276.7 kJ = 137.8 kJ .

So the final answer is that 137.8 kJ of energy has been lost due to friction.