A roller coaster needs 100,000 N of energy to make it over the next hill. It...

A roller coaster needs 100,000 N of energy to make it over the next hill. It starts at 110 m high from rest and falls to 10 m high from the ground. The coaster has a mass of 100 kg. The value of gravity is 9.8 m/s2, will the coaster make it? Why?

Solutions

Expert Solution

No, It will not

Explanation

I take it that the coaster needs 100,000J(Joule) of energy to cross the hill and not 100,000N(Newton) since J is the unit of energy and not N. N is the unit of force.

Let us assume that the coaster has 0 Joule(J) potential energy when it is at the ground level.

Then, when it is at a height of 110m from the ground , it will have a potential energy given by the formula

where,

V is the potential energy

m is the mass of the object(coaster).= 100kg

g is the accelaration due to gravity=9.8ms^-2

h is the height of the object from ground level

h1=110m

h2=10m

So , when the coaster went from h1 to h2, the chenge in potential energy is given by

Even if we assume that this is an ideal system and all the lost potential energy is translated into kinetic energy without any loss, this is still less than 100,000J, which the coaster requires to cross over the hill.

genius_generous answered 1 year ago

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