1. A 111 kg speaker with center of gravity G is supended by two vertical cables at D and E from a
truss. The truss is connected by a pin to bracket C, which is bolted to the ceiling. The truss is also
connected by a pin to bracket A, which is free to roll
Phys 170 Practice Final 2
Solutions
1. The massless semicircular plate with radius 1.5 m is supported by cables BD and CD and a ball
and socket joint A, and a load of 300 N is applied at the point shown. Find the tension in cables
BD and CD, and the compo
Phys 170 Practice Final 1 Solutions
1. How much force, applied horizontally at the axle, is required to make a 55.5 kg roller
with a 35 cm radius go over a 7.0 cm high obstacle?
(Hint: this becomes easy if you draw the right triangle)
R = 35 cm
r
F
h = 7.
Goals for Today
Review The Map
More Position as and Independent Variable
Velocity as Independent Variable
Piecewise Integration Pitfalls
There will be a quiz in tutorial on Tuesday
on 1-dimensional kinematics
Phys 170 Lecture 19
1
The Chain Rule of Differ
Goals for Today
Dynamics and the Rest of the Textbook
About Calculus
Kinematics in One Dimension, Acceleration (mostly) Constant
Administrivia:
There is a Mastering Enginering homework assignment,
due Saturday at 5:55 PM.
There will be normal ofce hours o
Lesson 5
Linear Equations and Matrices, and Matrix Multiplication
Entering Matrices
Solving Matrix Equations
Displaying the Last Column
Calcs Lesson 5
1
Linear Equations
A linear system is a set of equations with N variables times
constant coefcients,
Goals for Today
2D Rigid Body Equilibrium Examples
2-Force and 3-Force Members
Hinge and Bearing Alignment
3D Joint Forces and Moments
Start 3D Rigid Body Equilibrium
Phys 170 Lecture 13
1
Example Solution
!
FA
MC
!
F0
Find the reactions at A and B.
1. Un
Goals for Today
Midterm and other administrivia
Rigid Body Equilibrium Examples
Phys 170 Lecture 15
1
Midterm Info
We will skip Chapter 8 until after the midterm.
Midterm Exam: Friday Oct 10, regular class time
Bring 1 page of notes (both sides), handwrit
Goals for Today
Review of 2D moments
Right-Hand-Rule
Moments in 3D
3D Cross Product
Moment Around an Axis
Force-Couple and Couple-Moment
Phys 170 Lecture 10
1
Moment of a Force in 2D
M = RF sin ! = RF" = Fd = Rx Fy # Ry Fx
Use which ever is easiest, they
Goals for Today
Midterm Scores
Kinematics in 3D
Projectile Motion (constant acceleration + constant velocity)
Tangent-Normal Coordinates
Homework is due Saturday at 5:55 PM
Start it, so you have questions for
Ofce Hours, Thursday 10 AM - 1 PM
Phys 170 Lec
Goals for Today
Position as Independent Variable
Chain Rule
Differential Equations
Separate Variables and Integrate Both Sides
The Map
Administrivia:
There is a Mastering Enginering homework assignment,
due Saturday at 5:55 PM.
There will be normal ofce h
Goals for Today
More dynamics in xyz coordinates examples
Dynamics in normal-tangent coordinates
Quiz in tutorial Tuesday
Dynamics in xyz coordinates
Phys 170 Lecture 25
1
Example Problem
.
Block A weighs 10 lb, block B weighs 5 lb.
If both blocks start a
Goals for Today
More dynamics in normal-tangent coordinates
Dynamics in polar coordinates
Homework due Saturday 5:55 PM
Start it so you have questions for
Ofce Hours tomorrow, 10 AM - 1 PM
Phys 170 Lecture 26
1
Group Quiz 7
A skier travels down a slope wi
Goals for Today
Potential Energy
Conservation of Energy
Example Problems
Start Chapter 15: Impulse and Momentum
Homework due Saturday 5:55 PM
Start it before
Ofce Hours, Thursday 10 AM - 1 PM.
Phys 170 Lecture 29
1
Work and Energy in 3D
We integrate both
Goals for Today
Power & Efciency
Work & Energy in more than 1 dimension
Example Problems
No tutorial or quiz on Tuesday (Remembrance Day)
Homework due Saturday 5:55 PM
Start it before
Ofce Hours, Thursday 10 AM - 1 PM.
Phys 170 Lecture 28
1
Chapter 14: Wo
Goals for Today
Kinetics (dynamics - why things move)
Homework 7 due Saturday at 5:55 PM
Extra Ofce Hours: today, Pit Pub, 3-5 PM
Phys 170 Lecture 24
1
Chapter 13: Kinetics of a Particle
Kinetics means why things move the way they do
Dynamics is another w
Goals for Today
Relative Motion
Polar & Normal-Tangent Coordinates Revisited
Homework due 5:55 PM Saturday
Start it today, so you have questions for
Ofce Hours, Thursday 10 AM - 12:45 PM
Phys 170 Lecture 23
1
12.10: Relative Motion
Observer O is at the or
Goals for Today
Polar (Cylindrical) Coordinate Kinematics Examples
Pulleys
Relative Motion
Quiz Tuesday: 3D Kinematics (xyz, normal-tangent, polar)
Phys 170 Lecture 22
1
Velocity & Acceleration
in Cylindrical Coordinates
r = r ur + z uz
v = r ur + r u
Goals for Today
3D Joint Reactions (Forces and Moments)
3D Rigid Body Equilibrium Examples
Phys 170 Lecture 14
1
Joints in 3-D
Reaction at a joint includes both forces and moments.
Many students have trouble distinguishing the concept of
moment in a joint
Goals for Today
Tangent-Normal Coordinate Kinematics
Polar (Cylindrical) Coordinate Kinematics
Homework is due Saturday at 5:55 PM
Phys 170 Lecture 21
1
Kinematics in 3-D (xyz version)
!
j
Position becomes a vector: r = xi + y + zk .
Velocity is also a v
Goals for Today
Introduction to Rigid Body Equilibrium (Chapter 5)
2D Equations
2D Example
Choice of Reference Point
Forces and Moments at Joints in 2D
Example
Phys 170 Lecture 12
1
Chapter 5: Rigid Body Equilibrium
Rigid Body means
No longer just a poin
Goals for Today
Calculation Tools
Ill show MathStudio-online, and TI nSpire-CX-CAS here
TI-89, TI-83, HP-50g, MathStudio-tablet equivalents
are on the course web page
Vector Operations
Matrix Operations
Phys 170 Lecture 8
1
Computations In This Course
For
Lesson 3
Working with Degrees
More about getting decimal answers
R-Theta to Vector Function
R-Theta-Z to Vector Function
More about functions and programs
Calcs Lesson 3
1
TI-89 Titanium R-Th->V 1
Hit F1 for Tools and 8 for Clear Home
and [Clear] to
Lesson 5
Linear Equations and Matrices, and Matrix Multiplication
Entering Matrices
Solving Matrix Equations
Displaying the Last Column
Calcs Lesson 5
1
Linear Equations
A linear system is a set of equations with N variables times
constant coefcients,
Lesson 1
Entering vectors by components
Saving vectors in variable names
Adding vectors by name
Multiplying vector by scalar (non-vector)
Dot product of two vectors
Getting decimal answers
Saving les or deleting variables
Calcs Lesson 1
1
TI-83 Vec
Lesson 4
4-quadrant arc tangent
Vector to Theta-Angle Function
Calcs Lesson 4
1
MathStudio Tablet V->Th 1
Touch [le-menu] then [Open]
then functions.math to open our
le of functions.
Swipe the calc to get more
functions, touch in the empty
input box and
Lesson 1
Entering vectors by components
Saving vectors in variable names
Adding vectors by name
Multiplying vector by scalar (non-vector)
Dot product of two vectors
Getting decimal answers
Saving les or deleting variables
Calcs Lesson 1
1
MathStudi
Lesson 2
Dening and accessing your own functions and programs
Magnitude of a vector
Making a unit vector from a vector
Displaying a vector as a column
More about getting decimal answers
Calcs Lesson 2
1
MathStudio Web Functions 1
Go to http:/mathstud
Lesson 5
Linear Equations and Matrices, and Matrix Multiplication
Entering Matrices
Solving Matrix Equations
Displaying the Last Column
Calcs Lesson 5
1
Linear Equations
A linear system is a set of equations with N variables times
constant coefcients,
Phys 101 Experiment #2
Computer Graphing,
more HAND graphing,
and Buoyant Forces
Learning Goals
Why we use straight line fits:
Compile independent measurements into two parameters
(slope and y-intercept)
With straight lines it is easy to see expected t