Mechanical energy in situation 1 of the cart

[lamefeed]

Hi, I've been trying to figure out how to solve this problem for a few hours, but whatever I do it seems to give me the wrong answer.

Problem statement:
Fetch data from the roller coaster model. Ignore friction. What is the mechanical energy in cart in situation 1?

## E = E_k + E_p ##
Which gives me this formula
## E = \frac{1}{2}mv^2 + mgh ##
After this I remove the mass since it's not been given in the task, and I'm left with:
## E = \frac{1}{2}v^2+ gh ##
When I fill in the numbers I get this:
## E = \frac{1}{2}0.5^2 + 9.81*50 = 490 J ##But I'm supposed to get 49 J ?!

Can't get any help from my teacher until tomorrow so would be lovely if some of you could tell me where I took a wrong turn(If I made a mistake)!

Cheers,
Lamefeed

 

[mfb]

It is advisable to work with units, then the mistake would have been obvious as your units do not match.
You cannot "remove" a mass. The energy will depend on the mass, and if you do not know the mass it will stay as unknown parameter in the result.

If you are supposed to get 49 J then a mass of about 0.1 kg has to be given somewhere.

 

[lamefeed]

It is advisable to work with units, then the mistake would have been obvious as your units do not match.
You cannot "remove" a mass. The energy will depend on the mass, and if you do not know the mass it will stay as unknown parameter in the result.

If you are supposed to get 49 J then a mass of about 0.1 kg has to be given somewhere.

The mass is unknown. Can I by any stretch of the imagination get the mass? when I only know the velocity and the height?

 

[mfb]

No. I am 0.5 m above the ground, moving with a velocity of 0 m/s relative to it. What is my mass?

Is there some previous problem discussing a roller coaster where a mass might have been given?

 

[lamefeed]

Hehe, I get your point it's impossible to predict the mass with the velocity and height (:

This was the first task based on roller coasters, the next question was asking about the speed of the cart in situation 2..
This is a badly designed problem i guess..

 

[mfb]

Could be.

You can calculate the speed without knowing the mass, but not the kinetic energy in Joules.

 

[lamefeed]

I tried to do so but I ended up with ~19 m/s when the speed should have been 24 m/s. It was done without knowing that the mass should have been 0.1kg

 

[mfb]

The mass cancels in the calculation of the speed.
24.3 m/s is correct, how did you get 19?

 

[lamefeed]

that might have been a mistake on my end.

forgot to multiply by 2 in every part when I "made" up the formula.

Pardon my English as it's not my first language.