Problem 1-1 | General Principles | Engineering Mechanics: Statics | RC Hibbeler


Round off the following numbers to three significant figures: (a) 58 342 m, (b) 68.534 s, (c) 2553 N, and (d) 7555 kg.


Solution:

a) 58.3 km

b) 68.5 s

c) 2.55 kN

d) 7.56 Mg


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College Physics Problem 1.2.6


What is the height in meters of a person who is 6 ft 1.0 in. tall? (Assume that 1 meter equals 39.37 in.)


Solution:

First, convert 6 ft to inches

\displaystyle 6\:ft=\left(6\:ft\right)\left(\frac{12\:in}{1\:ft}\right)=72\:in

Add the 1.0 inch

\displaystyle 72\:in\:+1\:in=73\:inches

So, the total height of the person is 73 inches. We convert this to meters to come up with the desired unit.

\displaystyle 73\:in=\left(73\:in\right)\left(\frac{1\:m}{39.37\:in}\right)=1.85\:m

So, the height of the person is 1.85 meters.           ☚


 

College Physics Problem 1.2.2


A car is traveling at a speed of 33 m/s .
(a) What is its speed in kilometers per hour?
(b) Is it exceeding the 90 km/h speed limit?


Solution:

Part a

\displaystyle 33\:m/s=\left(33\:\frac{m}{s}\right)\left(\frac{1\:km}{1000\:m}\right)\left(\frac{3600\:s}{1\:hr}\right)=118.8\:km/hr

Part b

At 118.8 km/h, the car is traveling faster than the speed limit.


Important Concepts in Statics of Rigid Bodies

These points are taken from the book of Russel Hibbeler:

  • Statics is the study of bodies that are at rest or move with constant velocity.
  • A particle has a mass but a size that can be neglected, and a rigid body does not deform under load.
  • A force is considered as a “push” or “pull” of one body on another.
  • Concentrated forces are assumed to act at a point on a body.
  • Newton’s three laws of motion should be memorized.
  • Mass is a measure of a quantity of matter that does not change from one location to another. Weight refers to the gravitational attraction of the earth on a body or quantity of mass. Its magnitude depends on the elevation at which the mass is located.
  • In the SI system the unit of force, the newton, is a derived unit. The meter, second, and kilogram are base units.
  • Prefixes G, M, k, m, mu and n are used to represent large and small numerical  quantities. Their exponential size should be known, along with the rules for using the SI units.
  • Perform numerical calculations with several significant figures, and then report the final answer to three significant figures.
  • Algebraic manipulations of an equation can be checked in part by verifying that the equation remains dimensionally homogeneous.
  • Know the rules for rounding off numbers.

Geometry Basics

Geometry (from the Ancient Greek: γεωμετρία; geo- “earth”, -metron “measurement”) is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space (wikipedia.com).

Below are example questions in geometry basics. Take time to answer each of them. Afterward, you can download the answer at the bottom of the page.

Happy learning!

P1) The complement of an angle measures 56°. What is the measure of the angle?
a) 124º
b) 34º
c) 68º
d) 112º

Continue reading “Geometry Basics”