• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

Designing a Freight Elevator

Extracts from this document...



A heavy-duty freight elevator is used to raise and lower equipment and minerals in a mineshaft. Models are created to represent the movement of the elevator in terms of position. There are a number of specifications to take into consideration when creating a model and these will depend on the situation that the model is supposed to represent. To accommodate different specifications, different models are created with these specifications in mind.  

Analyzing a possible model

The formula y = 2.5t3 − 15t2 represents the position of the elevator, y, measured in meters (y = 0 represents ground level) and t represents time measured in minutes (t = 0 is the starting time). The trip up and down the shaft, ignoring time spent at the foot of the shaft, is approximately six minutes and that the depth of the shaft is no more than 100 meters.


By graphing the function (x = −1, y = 2.5t3 − 15t2) in parametric mode, one can better visualize the movement of the elevator down the shaft. The dot indicates where the function starts and stops as it runs from t = 0 to

...read more.




By changing to function mode, we can take a better look at the position, velocity, and acceleration of the elevator.

Position Function:


In the position graph above, we see that the elevator starts at ground level,  reaches a height of 80 meters below, and goes back up to up to ground level, all in the course of 6 minutes.

Velocity Function:


By taking the derivative of the position function (y = 2.5t3 − 15t2), we get the velocity function of y = 7.5x2 – 30x.  Velocity is the rate of change in position of the elevator. In the velocity graph, we see that the negative velocity means that the elevator is below ground level, which is arbitrarily labeled as y = 0. The velocity function matches the position function in indicating that the elevator goes down and then goes back up. The zero value of the velocity graph means that the elevator is stopped. The negative value means it is moving down away from ground level and the positive value means that it is going up moving towards ground level.  

Acceleration Function:


...read more.


y = 0 and y = 100. The number in front of the sin term determines the altitude and in turn how far down the elevator goes. For a different freight elevator, this number could to adjusted to fit how far that elevator will travel. The term in sin also determines the period, which would be how long a trip up and down would take. In the case of my model, the trip would take 4 minutes without any stops. This value multiplied by the variable determines this and can be changed to make the elevator go faster or slower. Making the model a piecewise function allows for sudden stops, which is hard to model in a single continuous function.

Applying the model

        This model may be further modified to fit a number of other situations. It can represent the up and down movement of other objects in life such as an airplane or rocket. One can use the strategies mentioned above to modify the period, altitude, and maximum and minimum to fit the situation that it calls for.

...read more.

This student written piece of work is one of many that can be found in our International Baccalaureate Maths section.

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related International Baccalaureate Maths essays

  1. A logistic model

    The interval of calculation is 1 year. Year Population Year Population 1 1.0?104 11 5.90?104 2 2.5?104 12 6.08?104 3 5.13?104 13 5.94?104 4 6.47?104 14 6.05?104 5 5.56?104 15 5.96?104 6 6.30?104 16 6.03?104 7 5.74?104 17 5.97?104 9 IB Mathematics HL Type II Portfolio: Creating a logistic model

  2. Math portfolio: Modeling a functional building The task is to design a roof ...

    able to calculate the ratio of wasted space to the volume of the office blocks for the structure height ranging from 36m to 54m. The above table shows that the ratio of the wasted space to the office block is the same for different height of the structure.

  1. The speed of Ada and Fay

    Diagram on finding Fay's position one From this diagram, it shows several points that I need to find before finding the coordinate of Fay's position in "F1" and "F2". There are several lines "A1F2", "A0F1", "A1F1", "Y2F2" and "X2F2". After calculating the distance of these lines, then I will have a very clear and accurate coordinates for Fay's position.

  2. Creating a logistic model

    Based on the values given in the table above, the calculator is able to estimate the logistic function of un+1. The function given by the calculator is: However, the function that the calculator gives is just an estimate, so it is safe for us to round off this function to:

  1. This paper attempts to analyze the formula modeling the motion of a freight elevator:

    From t = 2, a(2) = 0, this is when the velocity decreases, so it reflects the changes in the concavity of the velocity curve. From t = 2 to t = 4, the acceleration increases to positive values while the velocity values are still negative, this shows a decrease in speed of the elevator.

  2. Develop a mathematical model for the placement of line guides on Fishing Rods.

    Guide Number (from tip) 0* 1 2 3 4 5 6 7 8 n** Distance from Tip (cm) 0 10 23 38 55 74 96 120 149 230 *the guide at the tip of the rod is not counted **n is the finite value that represents the maximum number of guides that would fit on the rod.

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work