Ch. 9 Friction
Looking ahead:
9.1 Basic concepts.
Problems with one contact surface that slides.
Problems with multiple contact surfaces that slide simultaneously.
Tipping and sliding motion.
9.2 Problems with multiple contact surfaces.
9.3 Belts and c

6.4 Frames and machines
Frames and machines are structures that consist
of two or more members where one or more of
the members is a multi-force member (i.e., not a
two-force member).
Typically, a frame has full fixity and uses a stationary
arrangement o

Midterm 2 Logistics
Date: Tuesday, November 26th
Time: 5:45-7:00 pm or 7:30-8:45 pm
(your choice; no need to pre-register)
Location: 125 Ag Hall (125 Agriculture Hall) regardless of discussion day/time
Content: Chapters 1-7
Emphasis: Chapters 6-7
Midterm

2.5 Cross product
The cross product is useful for:
Determining a vector that is perpendicular to the plane containing
two other vectors.
Determining the moment of a force more on this in Chapter 4.
Cross product
The cross product between two vectors A a

Ch. 4 Moment of a Force &
Equivalent Force Systems
Looking ahead:
4.1 Moment of a force
(i.e., moment about a point)
4.2 Moment of a force about a line
4.3 Moment of a couple
4.4 Equivalent force systems
4.1 Moment of a force
The moment of a force (or si

2.4 Dot product
Or . how much of a vector acts
in a particular direction?
Example 1: A railcar needs to be moved along straight
level tracks. A locomotive is not available, so a truck and
chain will be used. The truck drives parallel to the tracks,
and th

2.3 Cartesian Representation of Vectors 3-D
A right-hand Cartesian coordinate system must be used:
unit
vectors
in 3D
v = vx + v y + vz
= vx i + v y + vz k
j
2
2
2
v = vx + v y + vz
Direction angles & direction cosines
Direction angles give the orientati

2.2 Cartesian Representation of Vectors 2-D
A Cartesian coordinate system has coordinate directions
that are orthogonal. Consider a vector v in this space.
v = vx + v y
= vx i + v y
j
v x is the component of v x in the i direction.
v y is the component o

Ch. 1 Introduction
Chapter Contents:
1.1 Engineering and Statics.
1.2 A Brief History of Statics.
1.3 Fundamental Principles.
1.4 Force.
1.5 Units and Unit Conversions.
1.6 Newton's Law of Gravitation.
1.7 Failure.
Please read all
sections.
We will cover

Statically indeterminate structures
. a brief introduction
A statically determinate structure has as many unknowns as
equilibrium equations generally, all of the unknowns can be
determined.
A statically indeterminate structure has as more unknowns than
eq

5.3 Additional Topics in Rigid Body Equil.
Topics:
Pulleys and cables
Springs and torsional springs
Supports and fixity
Statically determinate and statically indeterminate
bodies
Equation counting
Two-force members
Three-force members
Pulleys and c

6.2 Truss structures method of sections
Approach: Create a FBD of a portion of the structure by
making a cut through the member(s) whose forces we
want to determine. Where the cut passes through truss
members, include the forces supported by these
members

3.4 Engineering Design
Engineering Design is an iterative process consisting of
Identifying and prioritizing needs
Making value decisions
Applying the laws of nature to find solutions
The Process in Action
As engineering students, you apply this process e

EMA 201 Midterm 1
Thursday, October 10th
5:45pm or 7:30 pm
Location: depends on your discussion section
If your exam meets on
your exam room is
Monday or Wednesday
19 Ingraham Hall
Tuesday
5206 Social Sciences
Thursday
5208 Social Sciences
75 minutes long

4.4 Equivalent force systems
Consider designing the connection details
(e.g., bolts, welds, etc.) that connect the
wing and fuselage. It would be
inconvenient if the intricate details of the
air pressure distribution on the bottom
and top surfaces of the

4.3 Moment of a couple
Play movie:
Sec-4.3_1v1(twisting_of_pipe_ver_1)
Play movie:
Sec-4.3_2v1(twisting_of_pipe_ver_1)
4.3 Moment of a couple
A couple
produces only a
moment.
A couple has
no net force.
Couple
A couple is defined to be two forces with equa

EMA 201
Statics
Dr. Suzannah Sandrik
811 ERB
262-0764
sandrik@engr.wisc.edu
What is
Engineering Mechanics?
Engineering Mechanics
is a discipline that studies the response of solids,
structures, fluids and devices made of these materials to mechanical, the

4.2 Moment of a force about a line.
Frequently, we want the moment of a force about a line
or a specific direction.
In the vector approach, we use the cross product to
obtain the moment about some point (any convenient
point) on the line, followed by the

Support reactions
More detailed
discussion in Ch. 5.
Example 4: The driving mechanism for a steam locomotive
is shown. Piston A is acted upon by steam pressure p, which
drives piston rod AB. Plate B (called the cross head) slides without
friction on guide

Ch. 2 Vectors
Looking ahead:
2.1 Basic Concepts.
2.2 Cartesian Vector Representation in 2D.
2.3 Cartesian Vector Representation in 3D.
2.4 Vector Dot Product.
2.5 Vector Cross Product.
2.1 Basic Concepts
Definitions:
A scalar is a quantity that is complet

Two-force members
A member that has forces
at only two points, with
no moment loading and
no distributed forces, is
called a two-force
member.
Feature: The forces
supported by the member
have equal magnitude,
opposite direction, and
lines of action that a

7.2 Center of mass & center of gravity
Centroid
Depends on shape only.
Independent of density and gravity.
Center of mass
Depends on shape and density.
Independent of gravity environment.
Center of gravity
Depends on shape, density and gravity.
Also calle

Example 4 (continued from last time): The cross section of
a plastic channel is shown. Determine the area moment of
inertia about vertical axes through the centroid.
A: C is located 4 mm above the lower surface in center,
I x = 2048 mm 4 , I y = 23,550 mm

7.4 Distributed forces
Line force
A force distributed along a line is
called a line force, or a line load;
dimensions (force/length).
Surface force
A force distributed over an area is
called a surface force, or traction;
dimensions (force/area).
Volume fo

8.3 Relations among V, M, and w
FBD:
Equilibrium
of a small
piece of
beam:
F
y
= 0 : V V V w x = 0
V
= w
x
Take l im to obtain
x 0
dV
= w .
dx
x
M A = 0 : M + M + M V x + w x 2 = 0
M
x
=V w
x
2
dM
d2M
Take l im to obtain
= V . T hen
= w.
2
x 0
dx
dx
Dete

8.2 Internal forces in straight beams
Objectives:
Determine the internal forces V, M, and N everywhere
throughout a straight beam in 2D.
Draw the V and M diagrams.
Often, we want V, M, and N as functions of position x.
Sometimes, only the V and M diag

9.3 Belts & cables contacting cylindrical surfaces
Consider a flexible belt
or cable contacting a
cylindrical surface.
Let T2 and T1 be the values of force in the high tension
and low tension sides of the belt, respectively (T2 T1).
Even though the belt

Ch. 3 Equilibrium of Particles
Looking ahead:
3.1 Equilibrium of Particles in 2D.
3.2 Behavior of Cables, Bars and Springs.
3.3 Equilibrium of Particles in 3D.
3.4 Engineering design.
3.1 Equilibrium of particles 2D
Recall: Newton's laws of motion:
1st la