Physics 207: Lecture 2 Notes

1
Lecture 9

• Today
• Review session

Assignment For Thursday, Read Chapter 8, first
four sections Exam Wed., Feb. 18th from 715-845
PM Chapters 1-7 One 8½ X 11 note sheet and a
calculator (for trig.) Place Room 2103 All
Sections
2
Textbook Chapters

• Chapter 1 Concept of Motion
• Chapter 2 1D Kinematics
• Chapter 3 Vector and Coordinate Systems
• Chapter 4 Dynamics I, Two-dimensional motion
• Chapter 5 Forces and Free Body Diagrams
• Chapter 6 Force and Newtons 1st and 2nd Laws
• Chapter 7 Newtons 3rd Law
• Exam will reflect most key points (but not all)
• 30 of the exam will be more conceptual
• 70 of the exam is problem solving

3
The flying bird in the cage

• You have a bird in a cage that is resting on your
  upward turned palm.  The cage is completely
  sealed to the outside (at least while we run the
  experiment!).  The bird is initially sitting at
  rest on the perch.  It decides it needs a bit of
  exercise and starts to fly. Question How does
  the weight of the cage plus bird vary when the
  bird is flying up, when the bird is flying
  sideways, when the bird is flying down?
• So, what is holding the airplane up in the sky? 

4
Example with pulley

• A mass M is held in place by a force F. Find the
  tension in each segment of the massless ropes and
  the magnitude of F.
• Assume the pulleys are massless and
  frictionless.
• The action of a massless frictionless pulley is
  to change the direction of a tension.
• This is an example of
• static equilibrium.

5
Example with pulley

• A mass M is held in place by a force F. Find the
  tension in each segment of the rope and the
  magnitude of F.
• Assume the pulleys are massless and
  frictionless.
• Assume the rope is massless.
• The action of a massless frictionless pulley is
  to change the direction of a tension.
• Here F T1 T2 T3 T
• Equilibrium means S F 0 for x, y z
• For example y-dir ma 0 T2 T3 T5 and ma
  0 T5 Mg
• So T5 Mg T2 T3 2 F ? T Mg/2

6
Example

• The velocity of an object as a function of time
  is shown in the graph at right. Which graph below
  best represents the net force vs time
  relationship for this object? (E)

7
Another Example
A 200 kg truck accelerates eastwards on a
horizontal road in response to a gradually
increasing frictional force from the ground.
There is an unsecured 50 kg block sitting on the
truck bed liner. There is friction between the
block and the bed liner. An accelerometer is
mounted in the truck. The block accelerates with
the truck until the acceleration reaches 10 m/s2.
At that instant the block begins to slide and
the trucks accelerometer now reports a value of
11 m/s2. What are the coefficients of static
and kinetic friction? mS1.0 mk0.6
8
ExampleWedge with friction

• A mass m slides with friction down a wedge of
  angle q at constant velocity. The wedge sits at
  rest on a frictionless surface and abuts a wall.
  
• What is the magnitude of the force of the wall on
  the block?

FBD block
N
v
fk
m
q
mg
9
Example Wedge with friction
FBD block
fk

• A mass m slides with friction down a wedge of
  mass M angle q at constant velocity. The wedge
  sits at rest on a frictionless surface and abuts
  a wall.
• What is the magnitude of the force of the wall on
  the block?

N
mg
3rd Law
FBD wedge
-fk
Fw
-N
v
m
Mg
q
FF
10
Example Wedge with friction
FBD block
N

• A mass m slides with friction down a wedge of
  mass M angle q at constant velocity. The wedge
  sits at rest on a frictionless surface and abuts
  a wall.
• What is the magnitude of the force of the wall on
  the block?

fk
y
q
mg
x
x-dir S Fx 0 -fk mg sin q fk mg
sin q y-dir S Fy 0 N - mg cos q
N mg cos q
11
Example Wedge with friction

• A mass m slides with friction down a wedge of
  mass M angle q at constant velocity. The wedge
  sits at rest on a frictionless surface and abuts
  a wall.
• What is the magnitude of the force of the wall on
  the block?
• Notice that
• mg cos q sin q - mg cos q sin q 0 !
• Force wall 0
• But there are faster ways.

12
ExampleAnother setting

• Three blocks are connected on the table as shown.
  The table has a coefficient of kinetic friction
  of mK0.40, the masses are m1 4.0 kg, m2 1.0
  kg and m3 2.0 kg.

m2
T1
m1
m3
(A) What is the magnitude and direction of
acceleration on the three blocks ? (B) What is
the tension on the two cords ?
13
Another example with a pulley

• Three blocks are connected on the table as shown.
  The table has a coefficient of kinetic friction
  of mK0.40, the masses are m1 4.0 kg, m2 1.0
  kg and m3 2.0 kg.

N
m2
T1
T1
T3
m1
m2g
m1g
m3
m3g
(A) FBD (except for friction) (B) So what about
friction ?
14
Problem recast as 1D motion

• Three blocks are connected on the table as shown.
  The center table has a coefficient of kinetic
  friction of mK0.40, the masses are m1 4.0 kg,
  m2 1.0 kg and m3 2.0 kg.

N
m3g
m1g
T3
T1
m3
m1
m2
ff
frictionless
frictionless
m2g
m1g gt m3g and m1g gt (mkm2g m3g) and friction
opposes motion (starting with v 0) so ff is to
the right and a is to the left (negative)
15
Problem recast as 1D motion

• Three blocks are connected on the table as shown.
  The center table has a coefficient of kinetic
  friction of mK0.40, the masses are m1 4.0 kg,
  m2 1.0 kg and m3 2.0 kg.

N
m3g
m1g
T1
T1
T3
T3
m3
m1
m2
ff
frictionless
frictionless
m2g
x-dir 1. S Fx m2a mk m2g - T1 T3
m3a m3g - T3 m1a - m1g T1
Add all three (m1 m2 m3) a mk m2g m3g
m1g
16
Another example with friction and pulley

• Three 1 kg masses are connected by two strings as
  shown below. There is friction, , between the
  stacked masses but the table top is frictionless.
• Assume the pulleys are massless and frictionless.
• What is T1 ?

T1
friction coefficients ms0.4 and mk0.2
M
M
M
17
Chapter 2
18
Chapter 2
Also average speed and average velocity
19
Chapter 3
20
Chapter 3
21
Chapter 4
22
Chapter 4
23
Chapter 5
24
Chapter 5 6
25
Chapter 6
26
Chapter 7
27
Chapter 7
28
Short word problems

• After breakfast, I weighed myself and the scale
  read 588 N. On my way out, I decide to take my
  bathroom scale in the elevator with me.
• What does the scale read as the elevator
  accelerates downwards with an acceleration of 1.5
  m/s2 ?
• W (1.0-1.5/9.8) 588 N
• A bear starts out and walks 1st with a velocity
  of
• 0.60 j m/s for 10 seconds and then walks at
• 0.40 i m/s for 20 seconds.
• What was the bears average velocity on the
  walk?
• What was the bears average speed on the walk
  (with respect to the total distance travelled) ?

29
Conceptual Problem
The pictures below depict cannonballs of
identical mass which are launched upwards and
forward. The cannonballs are launched at various
angles above the horizontal, and with various
velocities, but all have the same vertical
component of velocity. (d)
30
Conceptual Problem
A bird sits in a birdfeeder suspended from a tree
by a wire, as shown in the diagram at left. (f)
Let WB and WF be the weight of the bird and the
feeder respectively. Let T be the tension in the
wire and N be the normal force of the feeder on
the bird. Which of the following free-body
diagrams best represents the birdfeeder? (The
force vectors are not drawn to scale and are only
meant to show the direction, not the magnitude,
of each force.)
31
Graphing problem
The figure shows a plot of velocity vs. time for
an object moving along the x-axis. Which of the
following statements is true? (C)
(A) The average acceleration over the 11.0 second
interval is -0.36 m/s2 (B) The instantaneous
acceleration at t 5.0 s is -4.0 m/s2 (C) Both
A and B are correct. (D) Neither A nor B are
correct.
32
Conceptual Problem
A block is pushed up a 20º ramp by a 15 N force
which may be applied either horizontally (P1) or
parallel to the ramp (P2). How does the
magnitude of the normal force N depend on the
direction of P? (B)

• (A) N will be smaller if P is horizontal than
  if it is parallel the ramp.
• (B) N will be larger if P is horizontal than if
  it is parallel to the ramp.
• (C) N will be the same in both cases.
• (D) The answer will depend on the coefficient of
  friction.

20
33
Conceptual Problem
A cart on a roller-coaster rolls down the track
shown below. As the cart rolls beyond the point
shown, what happens to its speed and acceleration
in the direction of motion (D)?
A. Both decrease. B. The speed decreases, but the
acceleration increases. C. Both remain
constant. D. The speed increases, but
acceleration decreases. E. Both increase. F. Other
34
Conceptual Problem

• A person initially at point P in the illustration
  stays there a moment and then moves along the
  axis to Q and stays there a moment. She then runs
  quickly to R, stays there a moment, and then
  strolls slowly back to P. Which of the position
  vs. time graphs below correctly represents this
  motion? (2)

35
The inclined plane coming and going (not
static)the component of mg along the surface lt
kinetic friction

• Exercise left for home but you should find that
  the block will always come to rest.
• Another type of problem
• A 8.0 kg rocket provides 80 N of thrust. A
  strong 10 m long rope is attached from a pivot to
  the rocket. If everything is horizontal and
  there is no friction describe the motion of the
  rocket from rest when the rocket has the
  following angles (90, 45 and 0 degrees).

36
Sample Problem

• A 200 kg wood crate sits in the back of a truck.
  The coefficients of friction between the crate
  and the truck are µs 0.9 and µk 0.5.
• The truck starts moving up a 20 slope. What
  is the maximum acceleration the truck can have
  without the crate slipping out the back?
• Solving
• Visualize the problem, Draw a picture if
  necessary
• Identify the system and make a Free Body Diagram
• Choose an appropriate coordinate system
• Apply Newtons Laws with conditional constraints
  (friction)
• Solve

37
Sample Problem

• A physics student on Planet Exidor throws a ball
  that follows the parabolic trajectory shown. The
  balls position is shown at one-second intervals
  until t 3 s. At t 1 s, the balls velocity is
  v (2 i 2 j) m/s.

a. Determine the balls velocity at t 0 s, 2 s,
and 3 s. b. What is the value of g on Planet
Exidor? -2 m/s2
38
Another question to ponder

• How high will it go?
• One day you are sitting somewhat pensively in an
  airplane seat and notice, looking out the window,
  one of the jet engines running at full throttle.
  From the pitch of the engine you estimate that
  the turbine is rotating at 3000 rpm and, give or
  take, the turbine blade has a radius of 1.00 m.
  If the tip of the blade were to suddenly break
  off (it occasionally does happen with negative
  consequences) and fly directly upwards, then how
  high would it go (assuming no air resistance and
  ignoring the fact that it would have to penetrate
  the metal cowling of the engine.)

39
Lecture 9
Assignment For Thursday, Read Chapter 8, first
four sections Exam Wed., Feb. 18th from 715-845
PM Chapters 1-7 One 8½ X 11 note sheet and a
calculator (for trig.) Place Room 2103 All
Sections