A 120-kg roller coaster cart is being tested on a new track, and a crash-test dummy is loaded into itThe roller coaster starts from rest at point A which is 35 m above the ground. The cart is observed to roll down the track to point Bwhich is 10 m above the ground . In your own words, what physics ideas would you be able to use to predict how fast the cart is moving at point B? What calculations would you use, what things would you be measuring , and what physics principles or laws would you use to make this calculation ?

a) variation of the energy is equal to the work of the friction force

b) W = Em_{f} -Em₀ ,  c) he conservation of mechanical energy

Explanation:

a) In an analysis of this problem we can use the energy law, where at the moment the mechanical energy is started it is totally potential, and at the lowest point it is totally kinetic, we can suppose two possibilities, that the friction is zero and therefore by equalizing the energy we set the velocity at the lowest point.

 Another case is if the friction is different from zero and in this case the variation of the energy is equal to the work of the friction force, in value it will be lower than in the calculations.

b) the calluses that he would use are to hinder the worker's friction force and energy

          W = Em_{f} -Em₀

          N d = ½ m v² - m g (y₂-y₁)

          y₂-y₁ = 35 -10 = 25m

c) if there is no friction, the physical principle is the conservation of mechanical energy

 If there is friction, the principle is that the non-conservative work is equal to the variation of the energy

carbon is found in all living things. carbon atoms move constantly through

living organisms, the oceans, the atmosphere, and the earth’s crust in what is

known as the carbon cycle. the directions taken by carbon atoms through this

cycle are very complicated and can take millions of years to make a full circle.

all animals, from humans to the dinosaurs are part of the carbon cycle. when

animals eat food, they get carbon in the form of carbohydrates and proteins.

in animals, oxygen combines with food in the cells to produce energy for daily

activity and then gives off carbon. the carbon combines with oxygen to form

carbon dioxide (co2) and is released back into the atmosphere as a waste

product when animals breathe and exhale.

from 145-65 million years ago, earth was much

hotter than today and covered with dense,

tropical swamp forests. the trees and other

plants were immense and

provided an endless supply of

food for the giant animals that

roamed the land. somewhere in

the air above one of these

forests, a lone carbon atom has joined

up with two oxygen atoms to form a molecule of co2.

the co2 molecule was sucked into the tiny holes (stomata) on the leaf of a

fern plant and joined with sunlight, chlorophyll and water to make food and

energy in the plant’s cells through photosynthesis. the oxygen (o2) from the

co2 molecule was sent back into the atmosphere; the carbon atom (c) was

detached and used to make a molecule of sugar.

if that carbon atom had been eaten instead, a totally

different situation would have developed. let’s say

that a giant plant-eating dinosaur (herbivore) ate the

fern for breakfast, and swallowed the carbon in the

fern in the form of carbohydrates and proteins. in

the process of respiration, oxygen combined with

the carbohydrates and proteins in the dinosaur’s cells

to provide energy for its daily activity.