Calculating Power Needed for Roller Coaster

[Photographer]

Homework Statement

I have a physics question that deals with power. In this problem it is of a roller coaster moving from 7m above ground to a point that is 90m above the ground.

1. What is the power needed for a roller coaster that needs to move 127m and is moving at a velocity of 3.5m/s? The mass of the vehicle is 2375kg and and retarding force on the train is 4225N.

M= 2375kg
F= I am not sure if it includes the 4225N or if I need to find it another way
D= 127
T=??

Homework Equations

Power= Work/Time
Work= Force * Displacement
Velocity= change in displacement/ time

The Attempt at a Solution

I did 4225*127/ 36.28 but I am not sure if the force is correct or the time...can someone please help!

 

[Redbelly98]

That is correct if the roller coaster moves along a level track. Yes, the time of 36 seconds is correct.

If the height of the roller coaster increases, that will require additional energy (and therefore additional power).

p.s. welcome to PF

 

[thomate1]

I would suggest approaching this problem by first identifying the relevant equations and variables. The power needed for a roller coaster can be calculated using the equation P = F * v, where P is power, F is force, and v is velocity. In this case, we have a retarding force of 4225N and a velocity of 3.5m/s. So, the power needed can be calculated as P = 4225N * 3.5m/s = 14,787.5 watts.

However, this only gives us the power needed to maintain a constant velocity. To calculate the total power needed for the roller coaster to move a distance of 127m, we need to take into account the work done. The work done is equal to the force multiplied by the displacement, or W = F * d. In this case, we have a displacement of 127m and a force of 4225N, so the work done is 4225N * 127m = 536,575 joules.

Now, to find the total power needed, we need to divide the work done by the time it takes to complete the distance. The time can be calculated using the equation v = d/t, where v is velocity, d is displacement, and t is time. In this case, we have a velocity of 3.5m/s and a displacement of 127m, so the time is 127m / 3.5m/s = 36.28 seconds.

Therefore, the total power needed for the roller coaster to move 127m at a velocity of 3.5m/s is 536,575 joules / 36.28 seconds = 14,787.5 watts. This is the same value we obtained earlier using the equation P = F * v.

I would also like to mention that the mass of the vehicle is not needed in this calculation, as power is independent of mass. The retarding force of 4225N is already accounted for in the calculation of work done.

I hope this explanation helps you understand how to approach and solve this problem. If you have any further questions, please feel free to ask.