Different observers can choose to use different coordinate systems. A frictionle

Question

Different observers can choose to use different coordinate systems. A frictionless roller coaster has been invented in which a single rider in a little cart can roll from the highest point to the lowest point picking up kinetic energy as it goes downhill. In the schematic of the roller coaster shown below, the struts are 4.00 meters apart and the cart and rider have a combined mass of 195 kg. What is the total mechanical energy of the cart-rider/Earth system according to Consuelo (an observer at the highest point on the track)? What is the total mechanical energy of the cart-rider/Earth system according to Mike (an observer at the ground level)? Do Consuelo and Mike agree on the value of the total mechanical energy? Why or why not? Do Consuelo and Mike agree that mechanical energy is conserved? Explain. Assuming that mechanical energy is conserved, what is the kinetic energy of the cart and rider when it rolls over the top of the second smaller hill?

Explanation / Answer

For Consuelo,

At the top,where he observes, the cart ride's height h=0.

Total energy of crtride/earth system according to him,

= K.E. + P.E.

=0+ m*g*h

=0 J

b. According to observer, Cart ride's height is h= 4*8=32 m, using conservation of energy,

Total energy of the system=K.E.+ P.E.

=0+m*g*h

=195*9.81*32 =612.14 kJ

c.Cusuelo and observer doesent agree beacuasse their reference cartesian system are diffrent.

d.For cousello, when he cart ride going @ the bottom, the energy will go in negative and it'll be the same as for observer, so they agree that way.

for Cousello,

mechanical energy @ top= 0

@ bottom= K.E. +m*g*h= 0 (h=-32m)

for observer,

P.E @ the top= K.E. @ the bottom.

So both agrees on conservation of energy.

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