Calculating a Zipline's Shape: Seeking Advice to Start Learning

[gelfer]

Hi

I want to understand how to describe the shape of a zipline given a certain mass at any point along that line and a difference in height of the Initial anchor point to the final anchor point.

I know that I don't know enough calculus to be able to work this out, but what I would like from this forum is to have a starting point (perhaps a formula so that i can break it down into parts) to begin my learning.

Advice on what areas I should begin to teach myself would be great!

Thanks for your help!

Greg

 

[jvicens]

Hi Greg,

To start, let's define some variables:

m = mass at any point along the zipline
h = difference in height between the initial and final anchor points
L = length of the zipline

The shape of the zipline can be described by its curve, which can be approximated by a parabola. This is because the force of gravity acting on the mass of the zipline creates a parabolic shape.

To begin your learning, I would recommend starting with basic calculus concepts such as derivatives and integrals. These will help you understand how to calculate the slope and area under a curve, which are important for describing the shape of the zipline.

Next, you can use the equation for the parabola, y = ax^2 + bx + c, to represent the shape of the zipline. The variables a, b, and c represent the coefficients that determine the specific shape of the parabola.

To find these coefficients, you will need to use the initial conditions of the zipline, such as the mass at the initial anchor point, the difference in height, and the length of the zipline. You can also use the equation for the parabola to calculate the slope and area under the curve at any point along the zipline.

I would also recommend learning about Newton's laws of motion and how they apply to the zipline, as well as concepts such as potential and kinetic energy.

I hope this provides a good starting point for your learning. Good luck!