Mathcad Worksheet 2 Starting to Walk

MathCAD worksheet 2 – Starting to walk

© dpl 2001, 3, 5,20061

PH15720 MathCAD Example Sheet 2

The aim of this worksheet is to introduce you to some more basic mathCAD concepts

By the end of the sheet you will know how to:

• Define variables in a mathCAD worksheet
• Choose acceptable names for physics problems
• Work with units
• Use text regions to explain your work

This worksheet takes the form of a number of examples which illustrate and introduce these principles. Work through them all.

Example 1 – Surface area and volume of a cylinder

This example is a simple worksheet to calculate the surface area and volume of a cylinder. It is based on the example on page 32 of the course text.

1. Log into the campus computer system
2. Start mathCAD
3. On the blank worksheet presented by mathCAD press “ to create a text region and type the following to describe the problem:
   Statement of problem
   Determine the surface area and volume of a cylinder with a radius of 7 cm and a length of 21 cm.
   
4. Enter the known values for the length and radius of the cylinder. Use rCyl and lCyl for the radius and length respectively.
   To enter the value for the radius type:
   rCyl:7*cm
   which mathCAD should display as rCyl := 7 cm
   Position the cursor underneath this line and enter the value of lCyl
5. Position the cursor to the right of the definition of rCyl and create a text box to explain that rCyl is the radius of the cylinder. Similarly create a text box to explain lCyl.
6. Enter the variable name aCyl by typing aCyl
7. Press : to define the variable aCyl MathCAD will insert a := sign
8. Now enter the equation for the area of a cylinder. To enter a  in mathCAD you can type <ctrl-shift-p> (keep the band j keys pressed until you let go of the p. To get the first part of the equation, for the area of the two ends of the cylinder you can type:
   2*<ctrl-shift-p>*rCyl^2
9. The selection box will be positioned around the 2, so press k to enclose the rCyl2 term
10. Add the second term by typing:
    +2*<ctrl-shift-p>*rCyl*lCyl

By now your result should look like this:

Having calculated the surface area of the cylinder and stored it in the variable aCyl, we can ask mathCAD to print it out. To do this, position the cursor below the bottom line of the sheet and type:
aCyl=

MathCAD will display the value of the variable acyl in its base units, which are m2 for area.

In order to display this result in cm2, select the placeholder (a black rectangle) that appears after the base units and type:

cm^2

and MathCAD will display the result in cm2:

In a similar fashion, create an expression to calculate the volume of the cylinder, vCyl and display the result in m3, cm3 and also cubic feet (ft3).

The following examples are based on the course text “An introduction to MathCAD 2000”, pp 36-43. You should get in the habit of using text areas to explain what you are calculating and also positioning the various regions of your calculation (text areas, comments, variable definitions, calculations and results) in such a way to make it clear what you are doing.

Example 2 – Unit conversions

Perform the following unit conversions:

In mathCAD13 c is already defined as the speed of light in a vacuum, so you should just print it out and then convert it to mph

Example 3 – More Volume & Surface Area Calculations

Calculate the volume and surface area of a sphere of radius 3 cm. The formulae you will need are:

The specific gravity of gold (Gold) is 19.32 gm/cm3. This can be found in the resource centre.

Calculate the mass of the 3 cm radius gold sphere. Display your answer in kg and also in lb.

Rho () may be selected from the Greek palette, or by typing r<ctrl-g>

Example 4 – Relating Force and Mass

MathCAD has a pre-defined constant, g, for the acceleration due to gravity.

A 150 kg mass is suspended from a hook by a wire of negligible mass. Use the equation of Newtons law to calculate the force acting on the hook.

The force on the hook is equal to the tension in the wire, in the case of a single wire. If two wires are used, the force on the hook is unchanged but the tension in each wire is halved. Calculate how many wires need to be used if the tension in each wire is not to exceed 300N

Example 5 - Spring Constants

Hooke’s law states that the extension of a spring, x, is linearly related to the force, F, applied to the spring.

where k is the spring constant. Use mathCAD to determine the spring constants for the following springs:

Example 6 – Chair Design

The backrest of a chair is spring loaded for comfort. The design specifications for a chair call for a maximum deflection of 5 cm when a 70kg person applies 40% of their body weight to the chair. (For this example assume that the weight is applied directly to the spring, without any intervening levers).

Use Newton’s law to determine the force applied to the backrest when a 70kg person leans 40% of their body weight against it.

Re-arrange Hooke’s law to determine the spring constant required for the spring in this case.

Using the spring specified in part b), determine the extension when a 90kg person leans 70% of their body weight against the backrest.

© dpl 2001, 3, 5,20061