Solving the Coaster Puzzle: Finding Variables and Calculations

[lidomonkee]

It's all still so confusing! Setting up the equation isn't the problem.. plugging in the numbers. I'm missing varibables and I don't know where to go to find themm

i. if the spring constant is 2000 N/m how far will the spring have to compress to bring the coaster to a stop? (Asume the weight of the coaster and passengers to be 45,000 N)

ii. if the spring dissipates half the available energy as heat, how far will your ride go *after released by the spring) before it stops or begins to roll forward? Show full calculations including point on scaled ddrawing of where the coaster would stop. (Don't forget friction)


I'm being told all these different equations KE = EPE + Heat
F = -kx F = kx Ke = (mv^2)/r I don't know what I'm doing at all

How do I find velocity?? it no where to be found, *sigh* so confused...

 

[futb0l]

i. $$F = kx$$
$$45000 = 2000x$$

ii. HINT: The potential energy of a spring is:
$$U = \frac{1}{2}kx^2$$

You should be able to figure it out.

 

[wais]

I completely understand your frustration. It can be overwhelming and confusing when trying to solve a physics problem, especially one involving multiple variables and equations. Let's break it down step by step to make it easier to understand and solve.

First, let's identify the given information and what we need to find. We are given the spring constant (k = 2000 N/m), weight of the coaster and passengers (W = 45,000 N), and the fact that the spring dissipates half the available energy as heat. We need to find the distance the spring will compress (x) and the distance the coaster will travel after being released by the spring (d).

Next, we need to understand the equations and variables involved. The equations you mentioned are all relevant to this problem. The first one, KE = EPE + Heat, represents the conservation of energy principle which states that energy cannot be created or destroyed, only transferred or transformed. KE represents kinetic energy, EPE represents elastic potential energy, and Heat represents the energy dissipated as heat. The second equation, F = -kx, represents Hooke's Law which relates the force (F) exerted by a spring to its spring constant (k) and the distance it is compressed or stretched (x). The third equation, KE = (mv^2)/2, represents the kinetic energy formula where m is the mass of the object and v is its velocity.

Now, let's solve the first part of the problem. We know that the coaster is brought to a stop by the spring, so the kinetic energy at the beginning (KE1) must equal the elastic potential energy at the end (EPE2). We can set up the equation as follows:

KE1 = EPE2 + Heat

We know that KE1 = (mv^2)/2 and EPE2 = (kx^2)/2, so the equation becomes:

(mv^2)/2 = (kx^2)/2 + Heat

We are given the values for m (45,000 kg) and k (2000 N/m), and we know that Heat is half the available energy, so we can substitute those values into the equation:

(45,000 kg)(v^2)/2 = (2000 N/m)(x^2)/2 + (1/2)(45,000 kg)(v^2)

Simplifying the equation, we get:

(1/2)(45