1. For a 20-m long rod. the density. (Ρ) and cross-sectional area, (A) changes along its length as follows:
| length, x (m) |
0 |
4 |
6 |
8 |
12 |
16 |
20 |
density, Ρ (g/cm3)
|
4 |
3.95 |
3.89 |
3.8 |
3.6 |
3.41 |
3.3 |
| area. A (cm2) |
100 |
103 |
106 |
110 |
120 |
133 |
150 |
What is the best estimate for total mass of the rod. [m = 0∫L(pA)dx]
2. The force on the mast (height, H) of a sailboat at any height, z above the boat deck is represented by f(z) = 200.(z/z+5)e-2z/H so that the total force will be F = 0∫H f(z)dz.
The point of application of (F) on the mast will be at a distance (d) from the base which can be calculated using the moment of the force as
d = 1/F [0∫H z. f(z) dz]
For H = 28. make the best estimates for (F) and (d) using 7 intervals.
3. The heat absorbed by a solar panel can be calculated from H = 0.45 0∫t qAdt
| t (hr): |
0 |
1 |
3 |
5 |
7 |
9 |
11 |
14 |
| q (cal/cm2/hr): |
0.1 |
5.32 |
7.8 |
8 |
8.03 |
6.27 |
3.54 |
0.2 |
Using the above data. determine the heat absorbed by a collector of A = 150000 cm2 during the 14-hr period.
4. The following formula has been developed relating vision loss (VL) and pressure inside the eye (p, mm Hg) for a person at any age (t, years) above the age of 25:
VL = 6.98301exp[0.009916 25∫t (p-13) dt
Determine the value of VL for a person of age 65, based on the following:
| age, t (yrs) |
25 |
40 |
50 |
60 |
65 |
| p (mm Hg): |
13 |
15 |
22 |
23 |
24 |