Transcript Chap 4:Dynamics: Newton`s Law of Motion

Chap 4:Dynamics:
Newton’s Law of Motion
Vector Kinematics
Generalizing the one-dimensional
equations for constant acceleration:
Projectile Motion
A projectile is an
object moving in two
dimensions under the
influence of Earth's
gravity; its path is a
parabola.
2D motion = two
independent 1D motions
Figure from “Conceptual Physics for Everyone”, Paul G. Hewitt, Addison Wesley, 2002.
Projectile Motion
It can be understood
by analyzing the
horizontal and
vertical motions
separately.
The speed in the x-direction
is constant; in the y-direction
the object moves with
constant acceleration g.
Projectile Motion
This photograph shows two balls
that start to fall at the same
time. The yellow ball has an
initial speed in the x-direction.
The vertical positions of the
two balls are identical at
identical times, while the
horizontal position of the
yellow ball increases linearly.
Solving Problems Involving Projectile
Motion
Example 3-6: Driving off a cliff.
A movie stunt driver on a motorcycle
speeds horizontally off a 50.0-m-high
cliff. How fast must the motorcycle
leave the cliff top to land on level ground
below, 90.0 m from the base of the cliff
where the cameras are? Ignore air
resistance.
Problem 31
(II) A fire hose held near the ground shoots
water at a speed of 6.5 m/s. At what angle(s)
should the nozzle point in order that the water
land 2.5 m away (Fig. 3–40)? Why are there two
different angles? Sketch the two trajectories.
Solving Problems Involving Projectile Motion
Example 3-7: A kicked football.
A football is kicked at an angle θ0 = 37.0° with a velocity
of 20.0 m/s, as shown. Calculate (a) the maximum height, (b)
the time of travel before the football hits the ground, (c)
how far away it hits the ground, (d) the velocity vector at
the maximum height, and (e) the acceleration vector at
maximum height. Assume the ball leaves the foot at ground
level, and ignore air resistance and rotation of the ball.
Problem 51
51. (II) A ball is thrown horizontally from
the top of a cliff with initial speed v0 (at
t=0). At any moment, its direction of
motion makes an angle θ to the horizontal
(Fig. 3–47). Derive a formula for θ as a
function of time, t , as the ball follows a
projectile’s path.
X and Y are Independent
•Red ball is dropped
vix=viy=0
White ball is tossed
horizontally viy=0 vix≠0
Yellow lines show equal
time intervals
.
Projectile Motion
If an object is launched at an initial angle
of θ0 with the horizontal, the analysis is
similar except that the initial velocity has
a vertical component.
Projectile
Motion
ay=g
ax=0
y
v
v0y
v0y
0

vix
v0 x  v0 cos
v0 y  v0 sin 
x
Solving Problems Involving
Projectile Motion
1. Read the problem carefully, and choose the object(s) you
are going to analyze.
2. Draw a diagram.
3. Choose an origin and a coordinate system.
4. Decide on the time interval; this is the same in both
directions, and includes only the time the object is moving
with constant acceleration g.
5. Examine the x and y motions separately.
6. List known and unknown quantities. Remember that vx
never changes, and that vy=0 at the highest point.
7. Plan how you will proceed. Use the appropriate equations;
you may have to combine some of them.
Solving Problems Involving
Projectile Motion
Projectile motion is motion with constant acceleration
in two dimensions, where the acceleration is g and is
down.
Relative velocity
Reference Frames
y
bug
vBA
car
vCA
x
Earth=A=stationary reference frame
vBA=velocity of the bug, B, relative to the earth, A
vCA= velocity of the lemon car, C, relative to the
earth, A
Relative velocity
y
A
bug
B
vBA
C
car
vCA
x
Earth=A=stationary reference frame
We can add reference frames to the bug, B and to
the Lemon car, C
vBA=velocity of the bug B, relative to the earth , A vBC=vBA-vCA
VCA=-VAC
Or
vBC=vBA+vAC
Notice how the outer subscripts on the right side of the equation correspond
with those on the left, and how the inner subscripts are the same but do not
exist on the left. Think of them as canceling.
Relative Velocity
Here, vWS is the velocity of
the water in the shore frame,
vBS is the velocity of the boat
in the shore frame, and vBW is
the velocity of the boat in the
water frame.
The relationship between the three
velocities is:
Chapter 4: Forces:
Defining Force
•Force = A push or a pull
•Units: Newtons = kg.m/s2
Two kinds of forces:
Long range: Gravitational force
Electromagnetic force
Contact: Everything else
Whenever two objects touch
Measuring Force
We can use a calibrated spring scale to measure
force
Force is a vector!
Net Force = the vector sum of all forces acting on
an object
Ah, but force is a vector.
Images: http://library.thinkquest.org/25844/dynamics/images/ski.gif;
http://www.mwit.ac.th/~physicslab/applet_04/physics_classroom/Class/vectors/u3l3b
Kinds of forces and
direction
Gravitational Force: (W) or Fg attraction
between earth and an object.
Forces on the
Most Common Contact Forces:
Friction: (f) parallel to contact surface
Normal: (N)
Perpendicula
r to contact
surface
Tension: (T) along rope or
cord or…
N
T
f
W
Problem 3
3. (I) What is the weight of a 68kg astronaut
(a) on Earth, (b) on the Moon g=1.7m/s2 , (c) on
Mars (g=3.7m/s2) , (d) in outer space traveling
with constant velocity?
Mass
Mass is the measure of inertia of an object; mass
is a measure of an object’s resistance to change
its velocity. In the SI system, mass is measured in
kilograms.
Mass is not weight.
Mass is a property of an object. Weight is the
force exerted on that object by gravity.
If you go to the Moon, whose gravitational
acceleration is about 1/6 g, you will weigh much
less. Your mass, however, will be the same.
Question
A UFO is hovering, stationary, 2000m
above the earth. The net force on the
UFO is
1) zero
2) due east
3) upwards
4) downwards
Question
An airplane is flying due East at a constant
velocity of 590 mph. The net force on the
airplane is
1) zero
2) due east
3) upwards
4) downwards
Question
The Earth travels around the Sun
with a constant speed. The net force
on the Earth is
a)zero
b)nonzero
Question
A skydiver is falling toward the
Earth at terminal velocity, that
is, at constant speed. The net
force on the skydiver is
a) zero
b) nonzero
Problem 7
7. (II) Estimate the average force
exerted by a shot-putter on a 7.0-kg
shot if the shot is moved through a
distance of 2.8 m and is released with a
speed of 13 m/s.
Newton’s First Law
of Motion
This is Newton’s first law, which is often called
the law of inertia:
Every object continues in its state of rest, or of
uniform velocity in a straight line, as long as no
net force acts on it.

F  0
Newton’s First Law of Motion
Inertial reference frames:
Newton’s first law does not hold in every
reference frame, such as a reference frame
that is accelerating or rotating.
An inertial reference frame is one in which
Newton’s first law is valid. This excludes
rotating and accelerating frames.
How can we tell if we are in an inertial
reference frame? By checking to see if
Newton’s first law holds!
Equilibrium
When the net force acting on an object is zero,
then it is in equilibrium.
åF
x
=0
and
åF
y
=0
and
åF
z
=0
An object in motion remains in motion
And An object at rest remains at rest
if the net external force acting on the object is zero. a=0, v=constant
Newton’s Second Law of
Motion
Example 4-2: Force to accelerate a fast car.
Estimate the net force needed to accelerate (a) a
1000-kg car at ½ g; (b) a 200-g apple at the same rate.
Example 4-3: Force to stop a car.
What average net force is required to bring a 1500-kg
car to rest from a speed of 100 km/h within a distance
of 55 m?
Problem 12
(II) How much tension must a
cable withstand if it is used
to accelerate a 1200kg car
vertically upward at 0.70m/s2
Problem 28
28. (I) Draw the free-body diagram for a basketball
player (a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–34.
Problem 37