Phys 103 Week 3
Vectors and
Vector Analysis
(N)
=10 m
=30 m
=15 m
30
(E)
Basic Trigonometry
Yes, high school math is s>ll relevant!
What are the three basic trig func3ons for angle ?
opp.
Rubber ball Example,
A 100 g rubber ball is dropped from a height of 2 m (~
6.5 ft) onto a hard floor. The plot below shows the force
that the floor exerts on the ball during contact. How
high does the ball bounce?
Fy
300 N
time
0.008 sec
Now that we have
Rubber ball Example,
A 100 g rubber ball is dropped from a height of 2 m (~
6.5 ft) onto a hard floor. The plot below shows the force
that the floor exerts on the ball during contact. How
high does the ball bounce?
Fy
300 N
time
0.008 sec
Law of Conservat
Explosion example
A 10 g projectile is traveling east at 2 m/s. When it
explodes into 3 pieces. A 3 g fragment is shot due west
at 10 m/s while another 3 g fragment travels 40o north of
east at 12 m/s. What are the speed and direction of the
3rd fragment?
The celestial Sphere
The celestial sphere appears to rotate about the Earth once every 24
hours from east to west on an axis through the north and south poles
of the Earth.
Relative to the stars, the Sun appears to move as
if it is attached to another sph
Consider two carts, of masses m and 2m, at rest on an air track (no friction).
And connected by a compressed spring. After release, the spring expands to
its equilibrium length, and the two carts moves apart. After the carts losses
contact with the spring
The formal definition of Newtons universal law of
gravitation is:
If two objects with masses M1 and M2 are a
distance r apart, then M1 will exert an attractive
force on M2, such that
Where is a radial unit vector directed from M 1 to
M2, and G is a consta
If you have a pulley system as shown below, and you pull the rope a length d,
how much does the mass raise?
A. d
B. 2d
C. 3d
D. d/2
E. d/3
If you have a pulley system as shown below, and you pull the rope a length d,
how much does the mass raise?
A. d
B.
Consider two carts, of masses m and 2m, at rest on an air track (no friction).
And connected by a compressed spring. After release, the spring expands to
its equilibrium length, and the two carts moves apart. After the carts losses
contact with the spring
The Center of mass of collection of particles is given by
Where
, the total mass of the system.
The total momentum of a collection of particles can be
calculated by multiplying the total mass of the system by
the velocity of the center of mass of the sys
Consider two carts, of masses m and 2m, at rest on an air track (no friction).
You push each cart for 3 sec, exerting equal force on each. At the end of 3 sec,
the momentum of the light cart is
A. the momentum of the heavy cart.
B. the momentum of the hea
Your friend gives a paperback book a push and sending it sliding along the
table toward you. When the book is halfway between you and your friend
(and still moving), which of the following is NOT a force that is acting on the
book?
A. Gravity
B. Friction
Car stunt example
A stunt man drives a car off a 10 m (~32 ft) high cliff at a
speed of 20 m/s (~ 45 mph). How far does the car land
from the base of the cliff?
Throwing and dropping balls
A heavy ball is thrown exactly horizontally at
height h above the
How to roughly estimate the radius of the Earth
while watching the Sun sets in West Texas ?
Suppose I am lying on the ground on a flat part of West Texas, and I am watching
the Sun sets over the horizon. Just as the top of the Sun disappears, I starts a
s
Two balls are thrown at the same time with the same speed from the ground.
One ball is thrown straight up and the other ball is thrown at an angle of 45o
above the horizon. Which ball hits the ground first?
A. The ball thrown straight up
B. The ball throw
Roller coaster question:
When a roller coaster car goes around a
vertical loop-the-loop of radius r, why
doesnt the car fall off at the top of the
circle?
Roller coaster question:
Is the motion uniform (constant speed) ?
What normal force does the car exp
Driving a car in the positive x direction at 60 MPH, Mary tests her brakes by
coming to a complete stop in 4 seconds. Then she resumes speed, taking 8
seconds to return to 60 MPH. A motion diagram is created by illuminating her
car with a strobe at 2 seco
1-D kinematics example
Consider an object whose position on the x-axis varies
with time according to the equation:
m 2
x 20m (50 2 )t
S
a) Find the objects displacement between ti = 1 sec
and tf = 2 sec.
b) Find the object average velocity during the time
Mass: Measured in kg, is an intrinsic
property of an object. An object has an
unique mass and it is always the same no
matter where in the universe it is.
Weight: Measured in N, changes depending
on the strength of gravity and whether or
not the object is
Wooden box on wood floor example:
I push a 50 kg wooden box across a wood
floor at a steady speed of 2 m/s.
(a) How much force do I have to exert on the
box?
(b) If Istop pushing, how far will the box slide
before coming to rest?
Assume for wooden objects
Child on a cart example:
A father places his 20 kg child on a 5 kg cart
to which a 2 m long rope is attached. He
then pushes the cart and child around in a
circle, keeping the rope parallel to the
ground.
If the father kept the tension in the rope at a
co
Work vs Power
Work is the transfer of energy to a body by
the application of a force over a distance.
Power tells you how quickly energy is
transferred to a body.
Why does the rate of energy transfer
matter?
Power = dE/dt
The unit of power is the Watt.
1
If two objects, with masses, m1 and m2 are
interacting with each other gravitationally, then
the change in potential energy as we move
the two objects relative to each other is given by:
So,
, and we chose to define the gravitational
potential energy of
Swing Rod Example:
A 1 m long, 200 grams uniform rod is hinged at one end
and connected to a wall. It is held out horizontally, then
released. What is the speed of the tip of the rod as it hits
the wall?
Assume the width and thickness of the rod is neglig
Which of the following is a representation of the vector shown?
y
4
A.-2+-2
3
B.-2+2
2
1
C.2+2
D.-2+3
E. None of the above
-5 -4 -3 -2 -1
-2
-3
1 2 3
x
Which of the following is a representation of the vector shown?
y
4
A.-2+-2
3
B.-2+2
2
1
C.2+2
D.-2+3
E
Many important application of rotational dynamics
involve objects, such as pulleys that are connected via
ropes or belts to other objects
If we say the rope turns on the pulley
without slipping, then that means
there is no relative motion between
the rim
Potential energy is conformational, it
describes the energy state of a system
based on the relative position of
different parts of a system.
Kinetic energy is motional, it describes
the energy state of a system based on the
relative motion of different
A force that changes magnitude with position:
The force from a spring, when the spring is
anchored at one end.
Suppose you have a spring whose equilibrium
length is ro. This is the length of the spring when it
is neither pushing nor pulling.
Lets define r
The potential energy of a certain system as a
function of position is given blow:
U(x)
x1
x2
x3
x4
x
The potential energy of a certain system as a
function of position is given blow:
U(x)
F
F
F
F
x1
x2
x3
x4
x
The potential energy of a certain system as a
In physics,
Work means the transfer of energy to a
body by the application of a force over a
distance.
Lets consider a force F, of magnitude |F|,
acting on a particle of mass m as the particle
is constrained to move along the x-axis from
an initial positi