Transcript Physics 106P: Lecture 1 Notes

Lecture 7: Introduction to Physics
PHY101
Chapter 2:
Free Fall (2.6)
Graphical Analysis of Velocity and
Acceleration (2.7)
Chapter 3:
Equations of Kinematics for Constant
Acceleration in 2 Dim. (3.1, 3.2)
Projectile Motion (3.3)
Physics 101: Lecture 7, Pg 1
Summary of Lecture 6

equations with constant acceleration (t0=0):

x = v0t + 1/2 at2

v = at

v2 = v02 + 2a x
• free fall: ay = -g = -9.80 m/s2

y = y0 + v0yt - 1/2 gt2

vy = v0y - gt

vy2 = v0y2 - 2gy
Physics 101: Lecture 7, Pg 2
Concept Question
Dennis and Carmen are standing on the edge of a cliff.
Dennis throws a basketball vertically upward, and at the
same time Carmen throws a basketball vertically downward
with the same initial speed. You are standing below the
cliff observing this strange behavior. Whose ball is moving
fastest when it hits the ground?
1. Dennis' ball
2. Carmen's ball
3. Same
Correct: v2 = v02 -2gy
Carmen v0
v0
Dennis
H
vA
vB
Physics 101: Lecture 7, Pg 3
Free Fall - Symmetry

At a given displacement along the path of motion the
magnitude of the upward velocity is equal the
magnitude of the downward velocity and they point in
opposite directions:
vup = - vdown
Physics 101: Lecture 7, Pg 4
Kinematics in Two Dimensions
Constant Acceleration
Consider an object which moves in the (x,y) plane from the initial
position r0, at time t0 with velocity v0, with constant acceleration.




position: your coordinates (just r=(x,y) in 2-D)
displacement: r = r-r0 change of position
velocity: rate of change of position
 average : r/t
 instantaneous: lim t->0 r/t
acceleration: rate of change of velocity
 average: v/t
 instantaneous: lim t->0 v/t
Same concepts as in one dimension !
Equations of kinematics are derived for the x and y components
separately. Same equations as in one dimension !
Physics 101: Lecture 7, Pg 5
Equations of Kinematics in 2 Dim.
Variable
x component
y component
Displacement  r
 x=x-x0
 y=y-y0
Elapsed time t (t0=0)
t
t
Initial velocity v0
v0x
v0y
Final velocity v
vx
vy
Acceleration a
ax
ay
 vx= v0x + ax t
 vy= v0y + ay t
x = x0 + t (vx+vx0)/2
y = y0 + t (vy+vy0)/2
x = x0 + v0 t + ax/2
t2
y= y0 + v0 t + ay/2 t2
vx2 = v0x2 + 2 ax x
vy2 = v0y2 + 2 ayy
Physics 101: Lecture 7, Pg 6
Eqs. of Kinematics in 2 Dim.


The motions along the x and y directions are completely
independent. They only share a common time.
Three swimmers can swim equally fast relative to the
water. They have a race to see who can swim across a river
in the least time. Relative to the water, Beth (B) swims
perpendicular to the flow, Ann (A) swims upstream, and
Carly (C) swims downstream. Which swimmer wins the
race?
A) Ann
B) Beth
C) Carly
correct
A B C
Time to get across = width of river / y-component of velocity
Physics 101: Lecture 7, Pg 7
Projectile Motion
A flatbed railroad car is moving along a track at constant
velocity. A passenger at the center of the car throws a ball
straight up. Neglecting air resistance, where will the ball land ?
1. Forward of the center of the car
2. At the center of the car
correct
3. Backward of the center of the car
Physics 101: Lecture 7, Pg 8
Kinematics of Projectile Motion (t0=0)

x direction : motion with constant velocity => ax = 0
x = x0 + v0xt
vx = v0x

y direction : free fall => ay = - g = -9.80 m/s
y = y0 + v0y t - 1/2 g t2
vy = v0y – g t
vy2 = v0y2 – 2 g (y-y0)
Physics 101: Lecture 7, Pg 9