Chapter 1-Statics

What is mechanics?

Mechanics is a branch of the physical sciences concerned with the state of rest or motion of bodies subjected to the action of forces.

What are the three main branches of mechanics?

Rigid-body mechanics, deformable-body mechanics, and fluid mechanics.

What is rigid-body mechanics (in this course/text)?

The study of bodies idealized as not deforming (shape does not change under load), used as a foundation for many engineering analyses.

What are the two areas of rigid-body mechanics?

Statics and dynamics.

What is statics?

Statics deals with the equilibrium of bodies: bodies that are either at rest or move with constant velocity (zero acceleration).

What is dynamics?

Dynamics is concerned with the accelerated motion of bodies (nonzero acceleration).

Why is statics sometimes considered a “special case” of dynamics?

Because statics corresponds to the case where acceleration is zero.

Why is statics taught separately in engineering?

Many engineered objects are designed to remain in equilibrium, so statics is heavily used in design and analysis.

What is an idealization (model) in mechanics?

A simplified representation of a real physical situation used to make applying theory easier.

What is a particle (idealization)?

A body with mass but negligible size; geometry/shape is ignored in the analysis.

When is it reasonable to model something as a particle?

When the body’s size is insignificant compared to the distances involved or when geometry does not affect the force/motion analysis.

What is a rigid body (idealization)?

A body modeled as many particles that remain at fixed distances from each other before and after loading (no deformation considered).

Why is the rigid-body assumption often acceptable?

Because many real engineering deformations are small enough that ignoring them still gives accurate force/motion predictions.

What is a concentrated force?

A force that represents a load assumed to act at a point on a body.

When can a load be treated as a concentrated force?

When the load acts over a very small area compared to the overall size of the body.

What are Newton’s laws used for in engineering mechanics?

They provide the experimental basis for formulating and solving mechanics problems.

What reference frame do Newton’s laws apply in (as stated)?

They apply to motion measured from a nonaccelerating reference frame.

State Newton’s First Law.

A particle at rest or moving in a straight line at constant velocity remains in that state unless subjected to an unbalanced force.

State Newton’s Second Law (concept).

An unbalanced force causes a particle to accelerate in the direction of the force, with magnitude proportional to the force.

State Newton’s Second Law (equation).

F=ma

State Newton’s Third Law.

Forces of action and reaction between two particles are equal in magnitude, opposite in direction, and collinear.

What is Newton’s Law of Universal Gravitation (equation)?

F = G \frac{m_1 m_2}{r^2}

What does $F$ represent in the gravitation law?

F is the magnitude of the gravitational force between the two particles.

What does $G$ represent in the gravitation law?

G is the universal gravitational constant (experimentally determined).

What value is used for $G$ in the text?

G = 66.73\times 10^{-12}\ \text{m}^3/(\text{kg}\cdot\text{s}^2)

What do $m1$ and $m2$ represent in the gravitation law?

m_1 and m_2 are the masses of the two particles.

What does $r$ represent in the gravitation law?

r is the distance between the two particles.

What is weight (in mechanics)?

The gravitational attraction of the earth on a body (a force).

How is weight related to mass near Earth’s surface?

W = mg

What is $g$?

g is the acceleration due to gravity.

Why is weight not an absolute quantity?

Because g depends on distance from Earth’s center (and thus elevation/position), so W=mg can change with location.

What is the “standard location” for $g$ used in typical engineering calculations (as stated)?

Sea level at a latitude of 45^\circ (standard location).

What value of $g$ is commonly used in SI calculations in this chapter?

g \approx 9.81\ \text{m/s}^2

What is the SI system?

The International System of Units (SI), a modern metric system used worldwide.

What are the SI base units for length, time, and mass (as stated)?

Meter (m), second (s), kilogram (kg).

What is the SI derived unit of force?

The newton (N).

Define the newton using base units.

1\ \text{N} = 1\ \text{kg}\cdot\text{m}/\text{s}^2

In SI, what is the weight of a 1 kg mass at standard gravity (using $g\approx 9.81$)?

W = mg = (1\ \text{kg})(9.81\ \text{m/s}^2)=9.81\ \text{N}

What is the U.S. Customary (FPS) system base set (as stated)?

Length in feet (ft), time in seconds (s), force in pounds (lb).

What is the derived unit of mass in the FPS system?

The slug.

Define the slug using FPS units.

1\ \text{slug} = 1\ \text{lb}\cdot\text{s}^2/\text{ft}

What value of $g$ is commonly used in FPS calculations in this chapter?

g \approx 32.2\ \text{ft/s}^2

How are the four basic quantities related so they are not all independent?

By Newton’s Second Law: F=ma (so force, mass, and acceleration are linked).

What are the four basic quantities emphasized for units in this chapter?

Length, time, mass, and force.

What is the idea of “base units” vs “derived units”?

Choose three base units (e.g., length, time, mass), then derive the fourth (e.g., force) using F=ma.

Give the direct conversion factor for force between lb and N (Table 1-2).

1\ \text{lb} = 4.448\ \text{N}

Give the direct conversion factor for mass between slug and kg (Table 1-2).

1\ \text{slug} = 14.59\ \text{kg}

Give the direct conversion factor for length between ft and m (Table 1-2).

1\ \text{ft} = 0.3048\ \text{m}

In FPS, what are common length/force multiples mentioned?

1\ \text{ft}=12\ \text{in},\quad 5280\ \text{ft}=1\ \text{mi},\quad 1000\ \text{lb}=1\ \text{kip},\quad 2000\ \text{lb}=1\ \text{ton}

What is a prefix in SI units?

A symbol that represents a multiple or submultiple of a unit (usually powers of 10).

What prefix is giga and what power of 10?

Giga (G) = 10^9

What prefix is mega and what power of 10?

Mega (M) = 10^6

What prefix is kilo and what power of 10?

Kilo (k) = 10^3

What prefix is milli and what power of 10?

Milli (m) = 10^{-3}

What prefix is micro and what power of 10?

Micro (\mu ) = 10^{-6}

What prefix is nano and what power of 10?

Nano (n) = 10^{-9}

What special note is given about the kilogram and prefixes?

The kilogram is the only base unit defined with a prefix.

SI rule: how do you separate multiple units to avoid confusion with prefixes?

Use a dot between units (e.g., \text{N}=\text{kg}\cdot\text{m}/\text{s}^2) so “m·s” isn’t confused with “ms”.

SI rule: what does an exponent on a prefixed unit apply to?

It applies to both the prefix and the unit (e.g., (\mu\text{N})^2 means the micro prefix is squared too).

SI rule: what is recommended about prefixes in denominators of composite units?

Avoid using a prefix in the denominator (except for kg); rewrite to move the prefix to the numerator (e.g., write kN/m instead of N/mm).

SI rule: what should you do with prefixes during calculations?

Convert prefixes to powers of 10 and work in base/derived units during computations.

What is dimensional homogeneity?

Every term in a physical equation must have the same units (dimensions), so terms can be meaningfully added/compared.

Give the kinematics example used to illustrate dimensional homogeneity.

s = vt + \frac{1}{2}at^2 (each term has units of length).

How can dimensional homogeneity help you check work?

If your algebra/manipulations produce terms with inconsistent units, something is wrong.

What are significant figures?

The digits in a number that reflect its measurement accuracy (how precise the number is).

Why can trailing zeros in a whole number be ambiguous for significant figures?

Because a number like 23400 might represent different precisions unless clarified.

How does engineering notation help with significant-figure ambiguity?

It expresses numbers in powers of 10^3 so the intended significant figures are clear (e.g., 23.4\times10^3 vs 23.400\times10^3).

Are leading zeros in numbers less than 1 significant?

No (e.g., 0.00821 has 3 significant figures).

General rounding rule (based on the next digit).

If the next digit is 5 or greater, round up; if it is less than 5, keep the digit the same.

Special rounding rule for a trailing 5 (as stated).

If the digit before 5 is even, do not round up; if the digit before 5 is odd, round up.

What is the best practice for intermediate results in multi-step calculations?

Do not round intermediate values; store them and round only the final answer.

What is the typical reporting convention for answers in this book (as stated)?

Report final answers to three significant figures (unless context demands otherwise).

What is the general procedure for analysis (first step)?

Read the problem carefully and connect the physical situation to the theory.

General procedure for analysis: what do you do with data and diagrams?

Tabulate given data and draw necessary diagrams (large, clear, properly labeled).

General procedure for analysis: what do you do with equations?

Apply relevant principles in mathematical form and ensure equations are dimensionally homogeneous.

General procedure for analysis: what do you do after solving?

Check that results are reasonable and consistent with the physical situation and units.

Key takeaway: mass vs weight.

Mass measures quantity of matter (does not change with location); weight is gravitational force and depends on location via W=mg.

Key takeaway: SI force unit classification.

The newton is a derived unit; meter, second, and kilogram are base units.

Key takeaway: what should you memorize from Newton’s laws?

Newton’s three laws of motion should be memorized.

Key takeaway: what should you know about SI prefixes?

Know G, M, k, m, \mu , n and their powers of 10, plus the rules for correct SI usage.

Key takeaway: how to check algebra in mechanics quickly.

Verify dimensional homogeneity (units match) as a partial check.