Total Mechanical Energy Problem

[Snape1830]

The 120 kg roller coaster just makes it to the top of hill A that is 15 m above the ground. It moves forward, picking up speed towards location B which is only 3 m above the ground. What is the total energy of the roller coaster as it passes location B, C, and D? Note: the velocity at the top of the hill is 0 m/s. The height of C= 8m and the height of D = 0 m. Ignore friction.

I know that total mechanical energy (TME) = PE + KE. However, I only have the velocity at the top of the hill and not at points B,C, and D. How do I find the velocity? I think I've done something like the Initial PE= final KE, but is that right? My teacher never told us that. Then further down on the questions it asks us to find the velocity of the roller coaster at these points, so is there a way to find TME without knowing the velocity? Do I use Work = change in kinetic energy?

Then another question asks us to find the kinetic energy at these points.

Please help I'm really stuck!

 

[gneill]

Without friction, total mechanical energy is a conserved quantity. What's the total mechanical energy at location A?

 

[Snape1830]

Without friction, total mechanical energy is a conserved quantity. What's the total mechanical energy at location A?

PE= mgh. So PE= 17640 JOhh I get it! So 17640=TME since kientic energy is 0 J. I completely forgot about that. Thanks!

 

[gneill]

PE= mgh. So PE= 17640 J


Ohh I get it! So 17640=TME since kientic energy is 0 J. I completely forgot about that. Thanks!

You're welcome.

 

[asteriatic]

Hello,

To calculate the total mechanical energy (TME) of the roller coaster at points B, C, and D, we first need to find the velocity at these points. We can use the principle of conservation of energy, which states that energy cannot be created or destroyed, only transferred from one form to another.

At point A, the roller coaster has only potential energy (PE) as it is at rest. As it moves down the hill, this potential energy is converted into kinetic energy (KE). At point B, the roller coaster has lost some potential energy but gained some kinetic energy. We can use the equation PE = mgh (mass x gravity x height) to calculate the potential energy at point A. Since the velocity at the top of the hill is 0 m/s, the kinetic energy at point A is also 0.

At point B, the roller coaster has lost 15 m of height, so the potential energy is now mgh = (120 kg)(9.8 m/s^2)(15 m) = 17,640 J. To find the velocity at point B, we can use the equation KE = 1/2mv^2 (1/2 x mass x velocity squared). We know the mass (120 kg) and the kinetic energy (17,640 J), so we can solve for the velocity: v = √(2KE/m) = √(2 x 17,640 J / 120 kg) = 14.7 m/s.

We can use the same process to find the velocity at points C and D. At point C, the height has decreased by 12 m, so the potential energy is now mgh = (120 kg)(9.8 m/s^2)(12 m) = 11,520 J. The velocity can be found using the same equation as before: v = √(2KE/m) = √(2 x 11,520 J / 120 kg) = 12.3 m/s.

At point D, the height has decreased by 8 m, so the potential energy is now mgh = (120 kg)(9.8 m/s^2)(8 m) = 9,600 J. Again, we can use the same equation to find the velocity: v = √(2KE/m) = √(2 x 9,600 J / 120 kg) = 10 m