ME 1020 Engineering Programming with MATLAB

Chapter 3 Homework Solutions: 3.4, 3.6, 3.10, 3.12, 3.16, 3.18, 3.24

Problem 3.4:

Create a vector for x over the range −2𝜋 ≤ 𝑥 ≤ 2𝜋. Use MATLAB to plot both sinh(x) and

(𝑒𝑥 − 𝑒−𝑥)/2 to show that they are the same function.

Problem 3.6:

The capacitance of two parallel conductors of length L and radius r, separated by a distance d in

air, is given by

𝐶 = 𝜋𝜖𝐿

ln[(𝑑 − 𝑟)/𝑟]

where 𝜖 is the permittivity of air (𝜖 = 8.854 × 10−12 F/m). Create a vector for d over the

range 0.002 ≤ 𝑑 ≤ 0.010 m. Use MATLAB to plot the capacitance over the range of d for L =

1 m and r = 0.001 m.

Problem 3.10:

An object thrown vertically with a speed v0 reaches a height h at time t, where

ℎ = 𝑣0𝑡 −1

2𝑔𝑡2

Create a Function File that computes the height h as a function of time 𝑡 for 𝑔 = 9.81 m/s2 and

𝑣0 = 50 m/s. Create a Calling Script File to plot the height versus the time 𝑡. Determine the

time when the object hits the ground using the fzero command.

Problem 3.12:

Problem setup:

𝐴 = 𝐿𝑊 +1

2𝐷2

𝐷2 + 𝐷2 = 𝑊2

2𝐷2 = 𝑊2

𝐷 =𝑊

√2;

1

2𝐷2 =

1

4𝑊2

𝐴 = 𝐿𝑊 +1

4𝑊2

𝐿 =1

𝑊(𝐴 −

1

4𝑊2)

𝐿total = 𝑊 + 2𝐿 + 2𝐷

Problem 3.16:

Problem 3.16: Scott Thomas

torus(a,b): a = inner radius (in); b = outer radius (in)

Problem 3.18:

Problem 3.18: Scott Thomas

Problem 3.24: