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Physics 151 Week 11 Day 2
Topics: Forces, Apparent Weight, & Friction
Energy
Dot Produce
Work
Conservation of Energy with Work
Work-Energy Theorem
Momentum
Conservation of Momentum
Collisions
1-D Collisions
2-D Collisions
Work and Impulse
Exam 2 comments:
Once exams are graded, I will make score adjustments as
needed if the class average is below normal for this class
due to time pressure.
However, in this class, you will be time limited on midterms
What can you do?
• Make sure you know and understand key concepts so you can
apply them quickly and correctly
• Practice doing homework problems with good solutions for time
=> this week, take 30 minutes, next week 25 minutes, next 20
minutes
• Read through the exam in the first minutes. Identify which parts
you can do quickly and well to maximize points
• Don’t rush. It’s better to do three parts well, then four parts badly
• If you don’t have time to finish a problem, tell me what you would
do if you had more time. More correct detail => more points
Course Grading
Every students’ overall score will be calculated two ways
1. As stated in the syllabus
2. By Exams only
• 2 best midterm scores
30% each
• Final Exam Score
Total
40%
100%
The higher overall score will be used to calculate your
grade. Note, over 95% of the time, syllabus grading will
result in the higher score. Homework scores correlate
strongly with exam performance.
Slide 4-19
Dot Product
Dot product or scalar product is a way of multiplying two
vectors to get a scalar result
Dot products can be calculated either independent of a
coordinate system where  is the angle between the two
vectors
r
r r
A  B  A B cos 
Note that in this case the sign of the dot product only
depends on the angle 
Or in component form
r
A  B  Ax Bx  Ay By  Az Bz
Slide 4-19
Dot Product: Example 1
Dot produce or scalar product is a way of multiplying two
vectors to get a scalar result
Dot products can be calculated either independent of a
coordinate system where  is the angle between the two
vectors
r
r r
A  B  A B cos 
Vector A has a magnitude of 4 units
Vector B has a magnitude of 3 units
Angle between them = 60 degrees
r
A  B  4 units  3units  cos(60)  6units
Dot Product: Example 2
Dot product or scalar product is a way of multiplying two
vectors to get a scalar result
Dot products in component form
r
A  B  Ax Bx  Ay By  Az Bz
Let
A  (1, 2, 3) and
So
r
AgB  1* 4  2 * 5  3* 6  32
B  (4, 5,6)
Slide 4-19
Example 3 Using a dot product to find angle
We know 2 ways to calculate the dot product
r
r r
A  B  A B cos 
r
A  B  Ax Bx  Ay By  Az Bz
Put these two equations for dot product = to each other
r
A B cos   Ax Bx  Ay By  Az Bz
Ax Bx  Ay By  Az Bz
r r
cos  
A B
Slide 4-19
Work
Definition of Work (in physics)
For constant Force
r
r r
r
Work W  F g r  F r cos 
Like all energy terms, work is a scalar
Work is the overall effect of a force applied over a
displacement. We can talk about the work done by
any force or the work done by the net force.
For non-constant force
Work = area under Fx vs. x graph
Note that work can be positive or negative
sign depends on cosine of angle between the vectors
Choosing the System
Slide 10-16
Work by an External Force
Conservation of Energy Equation
KEi + PEgi +Pesi + Esys = KEf + PEgf + Pesf +
Eth
Esys = Wext
where Wext = work done by external forces
Eth= - Wfriction
Slide 4-19
Sign of Work Questions
Answer these questions:
• For each of the forces,
in the force diagrams below,
the work done by that force is
(A) positive,
(B) negative,
(C) zero
(D) Can’t tell
Fn, tableM 1
Fnet, M 2
Fnet, M 1

FT ,stringM 2
FT , stringM 1

Fg, EarthM 1

Fg,EarthM 2


Slide 10-23
The Law of Conservation of Momentum
In terms of the initial and final total momenta:


Pf = Pi
In terms of components:
Slide 9-18
Slide 9-19
Summary
Slide 9-30
Elastic and Inelastic Collisions
Momentum is always conserved in collisions and explosions.
Elastic collision => momentum & mechanical energy are conserved
Inelastic collision => momentum conserved, mechanical energy is not
Mechanical Energy = KE +  PE
In an elastic collision, both objects return to their original
state (no change in shape, no deformation)
momentum & mechanical energy are conserved
In an inelastic collision, one or both objects deform and
change shape. Some mechanical energy goes into changing
the objects shape and is transformed into Ethermal
Inelastic collision => momentum conserved, mechanical energy is not
Inelastic Collisions
Momentum is always conserved in collisions and explosions.
Inelastic collision => momentum conserved, mechanical energy is not
First, we’ll consider perfectly inelastic collisions:
A perfectly inelastic collision results whenever the two objects
move off at a common final velocity.
Elastic Collisions
In an elastic collision, both momentum and mechanical energy are
conserved
Summary