Final velocity problem involving a roller coaster changing height

[AHUGEMUSHROOM]

A roller coaster (475kg) passes point C with a velocity of 10.0 ms-1, calculate the velocity of the roller coaster at point A.

mass = 475 kg
velocity at C = 10 ms-1
height at A = 30m
height at B = 0m
height at C = 25m
height at D = 12m

Ep = mgh
Ek = 1/2mv^2

The trolley is moving from Point C towards point A.

*My method of finding out the answer was incorrect so you might want to ignore the following*

I substituted the data given into Ep = mph (h at point A) and got Ep = 139,650J

Then said Ep = Ek and subbed the data into Ek and got final velocity = 24.5 ms-1


*THE CORRECT ANSWER IS THE SQUARE ROOT OF TWO*

 

[ehild]

Apply the conservation of mechanical energy. What does it say?

ehild

 

[AHUGEMUSHROOM]

I'm sorry but we have not come across mechanical energy yet and I am sure it was not used in working out the answer.

 

[ehild]

So what are Ep and Ek?

ehild

 

[rwisz]

I would approach this problem by using the conservation of energy principle. This principle states that energy cannot be created or destroyed, only transferred from one form to another. In this case, the potential energy (Ep) at point C is converted into kinetic energy (Ek) at point A.

First, we can calculate the potential energy at point C using the formula Ep = mgh, where m is the mass of the roller coaster (475kg), g is the acceleration due to gravity (9.8 ms-2), and h is the height at point C (25m). This gives us Ep = (475kg)(9.8 ms-2)(25m) = 116,875J.

Next, we can use the conservation of energy principle to equate Ep at point C to Ek at point A. This can be written as Ep = Ek. Substituting the values we know, we get 116,875J = 1/2(475kg)v^2, where v is the final velocity at point A.

Solving for v, we get v = √(2(116,875J)/475kg) = 24.5 ms-1. This is the correct answer for the final velocity at point A.

It is important to note that the height at point B is not relevant in this problem since the roller coaster is not moving at this point. We only need to consider the change in height from point C (25m) to point A (30m).

In conclusion, using the conservation of energy principle, we can calculate the final velocity of the roller coaster at point A to be 24.5 ms-1. This approach is more accurate and reliable than using incorrect methods or formulas.