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
Pure Translation Dynamics
Work & Energy with Rotation
Homework due 5:55 PM on Saturday
Start it so you have questions for
Ofce Hours, 10-12:30 Thursday
Phys 170 Lecture 35
1
Rigid Body Translation Without Rotation
Translation implies that
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
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
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
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
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
Fixed-Axis Rotation Dynamics
Translation+Rotation Dynamics
Pure Translation Dynamics
Last tutorial-quiz on Tuesday: Momentum and collisions
Homework due 5:55 PM on Saturday
Six of my previous nal exams are on the web site.
Solutions will g
Goals for Today
Finish dynamics in polar coordinates
Start Chapter 14: Work & Energy
Homework due Saturday 5:55 PM
Extra Ofce Hours, Pit Pub, 3-5 PM
Phys 170 Lecture 27
1
13.6 Kinetics in Polar/Cylindrical Coords
The
The
The
ur unit-vector points away fro
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
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
Goals for Today
2D Point Equilibrium Example
3D Point Equilibrium Example
Structure of the Equations
Linear Equations
Matrix Notation
Online Matrix Solvers
Phys 170 Lecture 7
1
Example Problem
1m
40
The spring has an unstretched
25 kg
length of 0.25 m and
Good Afternoon 170
How was your Christmas Break?
a)
b)
c)
d)
e)
Too hot.
Too cold.
Too short.
Too long.
Im freaking out!
1
Welcome to Physics 170
Statics and Dynamics
Dr. James Charbonneau
[email protected]
Irving K Barber 364
Hennings 329
2
The Standard
Setlist L3
Resolving a vectors. 3D vectors and direction angles
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
Wordle
Last class/this class: Components and the unit vectors i and j
Worksheet Week 1 [Q1]: Finding the missing magnitude using Polya.
Vectors in 3D: T
Physics 170 - Mechanics
Lesson 3
Sections 2.1-2.6
Mastering Engineering
Access codes are being sold again.
Students who buy the code separately from the Bookstore (without
buying the new text) must register at
https:/register.pearsoncmg.com/reg/register/r
Physics 170 - Mechanics
Lesson 5
Sections 2.7-2.9
Formula Sheets on Midterm
Recap and Preview
Last class
Position vectors
Displacement vectors
This class
Unit vectors (or directions along a force)
Dot products
Projections
Cables and Tension Force
B
r
THE UNIVERSITY OF BRITISH COLUMBIA
2015/2016 WINTER SESSION
MARCH EXAMINATION
PHYSICS 170 MECHANICS I
8:00 pm to 9:00 pm, Tuesday, March 22, 2016
MARKS
This exam counts for a total of 20 marks towards your Final Grade for the course.
The exam consists of
APSC 100 Module 1
Studio 3 Selection and Build
Week 4
Instructions
Write the names of the team members present in the space below. Respond to the studio tasks directly on this
worksheet. Add more rows if needed. When done, have one person from your team s