Conservation of Energy of park ride Problem

[Distance4life]

Homework Statement

A roller coaster travels on a frictionless track starting at point A, 5.0m off the ground. It then comes down to point B, 0.0m off the ground (it comes down to the ground), then it goes back up to point C, at 8.0m off the ground.

If the roller coaster is traveling at 5.0m/s at point A, what is the speed at point B?

Will it Reach Point C?

And lastly, What speed at point A is required for the roller coaster to reach point C?

Homework Equations

K=1/2mV²
U=mgh

The Attempt at a Solution

U₁ +K₁=K₂
U₂ +K₃=U₁ +K₁

K=1/2mV²
2K=mV²
2K/25.0m/s=m

Thats all I have, I seem to have trouble getting mass. Any help would be appreciated. Thanks

D4L

 

[Delphi51]

Energy at A = energy at B

On each side of the equation write in a .1/2mv² if it has KE and an mgh if it has PE. You should be left with only one unknown that you can solve for.

 

[kerimek]

1FE

As a scientist, it is important to recognize that the conservation of energy principle applies to this park ride problem. This principle states that energy cannot be created or destroyed, only transferred from one form to another. In this case, the roller coaster starts with potential energy at point A, which is then converted into kinetic energy as it travels down to point B. At point B, all of the potential energy has been converted into kinetic energy and the roller coaster is at its maximum speed. As it travels back up to point C, the kinetic energy is converted back into potential energy.

To solve for the speed at point B, we can use the conservation of energy equation: U1 + K1 = U2 + K2. At point A, the roller coaster has potential energy (U1) and kinetic energy (K1). At point B, it only has kinetic energy (K2) since it has reached the ground and all of the potential energy has been converted. Therefore, we can set up the equation as: mgh + 1/2mv^2 = 1/2mv^2. We know that the height at point A is 5.0m and the speed at point A is 5.0m/s, so we can plug in these values and solve for the speed at point B.

To determine if the roller coaster will reach point C, we can use the conservation of energy equation again. At point A, the roller coaster has potential energy (U1) and kinetic energy (K1). At point C, it has potential energy (U2) and kinetic energy (K2). If we set up the equation as: mgh + 1/2mv^2 = mgh + 1/2mv^2, we can see that the mass cancels out and we are left with the same equation as before. This means that the speed at point C will be the same as the speed at point B, which we solved for earlier.

To find the speed at point A that is required for the roller coaster to reach point C, we can use the conservation of energy equation once more. At point A, the roller coaster has potential energy (U1) and kinetic energy (K1). At point C, it has potential energy (U2) and kinetic energy (K2). If we set up the equation as: mgh + 1/2mv^2 = m