Welcome back to Physics 211

1
Welcome back to Physics 211

• Todays agenda
• Recap projectile motion
• Motion along curved paths, circles
• Tangential and radial components of acceleration

2
Current homework assignments

• WHW3
• In blue Tutorials in Physics homework book
• HW-19 1, HW-21 3, HW-21 4, HW-23 6
• due Wednesday Sept 20th in recitation
• No FHW this week (FHW2 will be assigned tomorrow
  and due 2 weeks later)
• Finish 2D Motion worksheets from yesterday and
  discuss with TAs and coaches on Friday

3
Exam 1 next Thursday (9/21/06)

• Seating arrangement will be posted outside
  Stolkin
• Material covered
• Textbook chapters 1, 2, and 3
• Lectures up to 9/19 (slides online)
• Tutorials on Velocity, Acceleration in one
  dimension, and Motion in two dimensions
• Problem Solving Activities 1, 2, and 3 (on
  Graphs, Vectors, and Problems on motion in two
  dimensions)
• Homework assignments

4
Preparing for exam

• Review homework problems and worksheets from
  recitation workshops
• Work through practice exam problems (posted on
  website)
• Work on more practice exam problems next
  Wednesday in recitation workshop
• Try extra end-of-chapter problems in textbook

5
A battleship simultaneously fires two shells at
enemy ships. If the shells follow the parabolic
trajectories shown, which ship will be hit
first? 1. A 2. Both at the same
time 3. B 4. need more information
6
Projectile motion
y
x
R when is y0 ?
tvy1-(1/2)gt 0
?
i.e. T (2v)sinq/g
7
Motion on a curved pathat constant speed
Is the acceleration of the object equal to zero?
8
Velocity is tangent to path
Ds
sI
sF
O
v Ds/Dt lies along dotted line. As Dt ?
0 direction of v is tangent to path
9
Motion on a curved pathat constant speed
10
For an object moving at constant speed along a
curved path, the acceleration is not zero.
11
A child is riding a bicycle on a level street.
The velocity and acceleration vectors of the
child at a given time are shown. Which of the
following velocity vectors may represent the
velocity at a later time?
a
1. 2. 3. 4.
12
A biker is riding at constant speed clockwise on
the oval track shown below. Which vector
correctly describes the acceleration at the point
indicated?
13
Biker moving around oval at constant speed
As point D is moved closer to C, angle approaches
90.
14
Acceleration vectors for car moving on
peanut-shaped track at constant speed
15
Summary

• For motion at constant speed, instantaneous
  acceleration vector is perpendicular to velocity
  vector
• Points inward
• What is the magnitude of the acceleration vector?

16
Acceleration vectors for ball swung in a
horizontal circle at constant speed v
v1
v2
R
q
v1
q
v2
What is the magnitude of the acceleration??a?
v2/R
17
Acceleration of object moving at constant speed
on a circular path
Acceleration depends on radius of circle.
18
Two cars are moving at different constant speeds
on a curved road. One after the other, they are
passing the same point on the road Car A at 18
mph car B at 36 mph. If car As acceleration is
2 m/s2, car Bs acceleration is
1. 1 m/s2 2. 2 m/s2 3. 4 m/s2 4. 8 m/s2
19
A ball is rolling counter-clockwise at constant
speed on a circular track. One quarter of the
track is removed. What path will the ball follow
after reaching the end of the track?
20
demo

• Circular track and ball remove section

21
What is the magnitude of the acceleration of an
object moving at constant speed if the path is
curved but not a circle?
r is the radius of curvature of the path at a
given point
22
Radius of curvature

• The radius of a circle which just touches the
  curved path at that point.

r
Radius of curvature r
23
Acceleration vectors for object moving around
oval at constant speed
24
What if the speed is changing?

• Consider acceleration for object on curved path
  starting from rest
• Initially, v2/r 0, so no radial acceleration
• But a is not zero ! It must be parallel to
  velocity
• a Dv/Dt rate of change of speed

25
Motion on a curve with changing speed

• Alternatively consider path with very large
• radius of curvature ? zero radial accel.
• Motion looks 1-dimensional.
• Therefore remaining acceleration must be along
  direction of velocity and measures rate of change
  of speed.

26
Acceleration vectors for object speeding
upTangential and radial components(or parallel
and perpendicular)
27
Sample problem
A Ferris wheel with diameter 14.0 m, which
rotates counter-clockwise, is just starting up.
At a given instant, a passenger on the rim of the
wheel and passing through the lowest point of his
circular motion is moving at 3.00 m/s and is
gaining speed at a rate of 0.500 m/s2. (a) Find
the magnitude and the direction of the
passengers acceleration at this instant. (b)
Sketch the Ferris wheel and passenger showing his
velocity and acceleration vectors.
28
Summary

• Components of acceleration vector
• Parallel to direction of velocity
• (Tangential acceleration)
• How much does speed of the object increase?
• Perpendicular to direction of velocity
• (Radial acceleration)
• How quickly does the object turn?

29
Acceleration vectors for object moving around
oval while speeding up from rest
30
Car going through loop-the-loop
31
Acceleration vector for object speeding up from
rest at point A ?
32
Vector components in 2D motion

• To study 2D motion, can resolve all vectors into
  components. Two different methods
• Cartesian (projectile motion)
• Radial/tangential circular motion, general
  motion on curved paths
• Either can be used. Choose easiest method for
  particular problem.

33
Reading assignment

• Relative motion
• 3.5 in textbook
• Review for Exam 1 !