Phy 2053 Announcements
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Homework (“intro to webassign”) due
tomorrow at 11:59pm is practice and not for
credit. You can access homeworks without
having a registration code (until Jan 17th).
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Homework 1 due Jan 21 is posted in
webassign. It will count towards course grade.
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Solution manual: We are working with UF
bookstore to order them for you to purchase.
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Yellow book (past exams and solutions)
available at Target Copy for $16
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Clicker questions will count towards course
grade starting Jan 27.
Instantaneous Velocity:
keep making ∆t smaller:
∆x
∆t
The slope of the line tangent to the position-vs.time graph is defined to be the instantaneous
velocity at that time
Acceleration
„
„
„
∆t
VAB = ∆XAB/∆tAB = (Xf-Xi)/∆t = (54 m - 30 m)/10s = 2.2 ms-1
Typical Homework Problem
2.19
Runner A is initially 4.0 mi west
of a flagpole and is running with a
constant velocity of 6.0 mi/h due east.
Runner B is initially 3.0 mi east
of the flagpole and is running with a
constant velocity of 5.0 mi/h due
west. How far are the runners from the
flagpole when they meet?
Let’s pick it apart
Average Acceleration
Changing velocity means an
acceleration is present
Acceleration is the rate of change of the
velocity
a=
„
Average vs. Instantaneous Velocity
Average velocity between
A and B
v
∆x
∆x
v
vaverage =
∆t
∆v v f − v i
=
∆t
tf − ti
Units are m/s² (SI), cm/s² (cgs), and
ft/s² (US Cust)
Vector quantity
1
Instantaneous acceleration
= slope of tangent of velocity-time graph
Position (m)
velocity (m/s)
acceleration (m/s2)
Acceleration
„
„
„
„
„
When the sign of the velocity and the
acceleration are the same (either positive or
negative), then the speed is increasing
When the sign of the velocity and the
acceleration are in the opposite directions, the
speed is decreasing
Kinematic Equations
Used in situations with uniform
acceleration
v = v o + at
∆x = v o t +
A negative acceleration does not
necessarily mean the object is slowing
down
If the acceleration and velocity are both
negative, the object is speeding up
(1)
1 2
at
2
v 2 = v o2 + 2 a∆ x
(2)
(3)
⎛ v + vf ⎞
∆x = v average t = ⎜ o
⎟t
⎝ 2 ⎠
Important: use the correct sign for x, v and a.
Some examples of Use
∆x = v average
Acceleration not in equation
⎛ v + vf ⎞
t=⎜ o
⎟t
⎝ 2 ⎠
Free Fall
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„
Displacement not in equation:
v = vo + at
Final velocity not in equation :
∆x = v o t +
1 2
at
2
„
If only force on object moving near surface of
earth is gravity it is in free fall
Free fall is constant acceleration
The acceleration is called the acceleration due
to gravity, symbolized by g
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g = 9.80 m/s²
„
g is always directed downward
„
„
Time not in equation :
v 2 = v o2 + 2a∆x
„
„
When estimating, use g ≈ 10 m/s2
toward the center of the earth
Ignore air resistance and assume g doesn’t
vary with altitude over short vertical distances
Forces can apply to the object before or after the free fall
2
Free Fall options
• Initial velocity is zero
Problem-Solving Hints
„
v=0
• Throw up -initial velocity
non-zero and positive—
instantaneous velocity at
maximum height = 0
• Throw down –initial
velocity is negative
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„
„
Convert if necessary
Choose the appropriate kinematic equation
Solve for the unknowns
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„
Choose a coordinate system, label initial and final
points, indicate a positive direction for velocities and
accelerations
Label all quantities, be sure all the units are
consistent
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„
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• Starting and ending heights may
be equal – symmetric or
not equal-asymmetric - trajectory
Read the problem
Draw a diagram
You may have to solve two equations for two
unknowns
Check your results
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„
Estimate and compare
Check units
A Typical Problem
2-53. A model rocket is launched straight
upward with an initial speed of 50.0 m/s.
It accelerates with a constant upward
acceleration of 2.00 m/s2 until its engines
stop at an altitude of 150 m. (a) what
can you say about the motion of the
rocket after its engines stop? (b) What is
the maximum height reached by the
rocket? (c) How long after lift-off does
the rocket reach its maximum height? (d)
How long is the rocket in the air?
3