Finding speed of roller coaster at different points

[joe426]

Homework Statement

Homework Equations

KE= 1/2 m v²
PE = mgy

The Attempt at a Solution

I'm not sure how to start this because there is no given mass. If I use a kinematics equation I don't have an acceleration.

 

[cbasst]

At point 1, the roller coaster only has potential energy (no kinetic energy because velocity is 0). At point 2, it will have lost all of its potential energy - the potential energy will have been converted into kinetic energy. Since no energy is being lost due to friction, PE₁ must be equal to K₂. Given that, can you figure the rest out? (Hint: set up the equation PE₁=K₂)

 

[joe426]

v = sqrt (2gy)
v = sqrt (2 * 9.8m/ss * 35m) = 26.19 m/s at point 2

But K₂ doesn't equal P₂ because K₂ equaled P₁ at a height of 35m, not 28m, right?

 

[cbasst]

But K2 doesn't equal P2 because K2 equaled P1 at a height of 35m, not 28m, right?

I don't know if I understand this question. Did you mean to say "But K2 doesn't equal P3 because K2..."? If you were asking about how to solve for velocity at P₃, do you think you could use a similar strategy that you did for point P₂? It may help if I point out that you are indirectly given the difference in height between P₁ and P₃.

 

[Nickie]

To find the speed of a roller coaster at different points, you would need to know the mass of the roller coaster, as well as its potential and kinetic energy at each point. Without this information, it is not possible to accurately calculate the speed of the roller coaster.

One way to approach this problem would be to collect data on the roller coaster's position at different points and use that information to plot a graph of its velocity over time. This would give you an idea of the roller coaster's speed at different points, but it would not give you an exact numerical value.

Additionally, you could also use a motion sensor to track the roller coaster's position and velocity at different points. This would give you more accurate data to work with, but you would still need to know the roller coaster's mass in order to calculate its speed using the equations provided.

In summary, to accurately determine the speed of a roller coaster at different points, you would need to know the roller coaster's mass, as well as its position and velocity at those points. Without this information, it is not possible to provide a specific solution to this problem.