Forces
Newtons Laws
1st Newtons Law
An object at rest stays at rest. An object in motion continues its motion at a constant
velocity i.e. at constant speed and in a constant direction.
or
If the net force on an object is zero, then the object will stay at
m. will an my [re who em
Two boxes m1, and m2 are connected by a string
through a pulley. Both string and pulley can be
assumed to be massless, while the masses of box
m1, and box m2 are given in the picture on the
righthand side. Box m1 is on a horizon
Problem with Pipe . long
. ii vertical
" tube
In the picture, you can see a pipe with a valve on the
left, valve 1, and one on the right, valve 2. A small
open tube extends upwards from the lower section of
the pipe without disturbing the stream line ow
Problem with 2 Masses It. kw
In the gure, the string and the pulley are massless, and there is no
friction either between the shaft of the pulley and the pulley or be-
tween the box m2 and the surface on which it placed
a) Set up two equations that desc
722,222 Review win aejcltogl
Santa is tired of sliding down chimneys, so for the next house, he decides to simply throw his
presents frOm his sled to the house 5 chimney. As shown in the picture below, the opening of the
chimney of the house IS at a heigh
Vilmawlz ll
Problem on Angular Momentum and Angular Impulse
A wheel has a moment of inertia of 0.7kgm2. The radius of the wheel is R=0.07m. If the wheel is
turning at an angular velocity of 90rad/s, what is the value of the minimum force we need to ap-
pl
WEST 90me 9in (M973 cud @993; [00% 991% Hats #14
Two boxes and one pulley are arranged as shown in the picture on the side.
Theb'oxes have masses m1=1.3kg and m2=2kg and they are hanging down
from the pulley connected through a massless string. The pulley
U M l
' r (5* WW;
Problem with Spring and Sogair Gun cfw_x mm, tumW, ><
' \
We want to measure the muzzle velocity of a Soilatrmpellht of mass mp=3 g. The muzzle veloc-
ity is the speed a projectile has at the moment it leaves the muzzle, i. e. the end
M
Problem on Finding Motion Through Integration
An object has an acceleration a=k*t, Where k=2m/s3. At t"Os, it is at a position xo=3m and has a
velocity of v0=5m/s.
a) What is the velocity of the object at F153?
m: 23 AL I
t=03
July 1 1
tdt- ll 21:) y: 2
Homework 14
Due Monday, November 30, 2015, in recitation
Problem with Carnot Cycle
N.B.: In your answer always clearly show the sign of
your numerical result!
1105
8104
Pressure in Pa
One mole of an ideal monoatomic gas has volume of
V1=0.03m3 and it is a
Homework 8
Due Monday, October 19, 2015, in recitation
Test Problem with Collision in 2D #3
Puck A and B have the same mass mA=mB=m=0.5kg. Pucks A and B rest on ice, and we can assume there is no friction between the pucks and the ice. Puck A hits puck B
Homework 1
Distance traveled versus Displacement
A girl walks 50m towards east and then 70m towards west.
What is her distance traveled?
50We~ iiOtwi: ('20! y
+ $0M (70 w) = - 20w (20w amin>/.
In 20 seconds, a girl walks 50m towards east and then, in 14
Homework 5) i:
Problem with Energy, and more than one Body #1 _
In the gure on the left hand side, the
strings and the pulleys are massless,
and there is no friction either between
the shaft 0f the pulleys and the pulleys
or between the boxes and the surf
Kinematics
Translational Motion in 1-Dimension
In translational motion, the object that is moving does not rotate.
Distance traveled and displacement are not the same thing:
Distance travelled is a scalar, while
displacement is a vector, it has
magnitude
Motion of The Rigid Body
A rigid body is a solid object extended in space that does not change its size or its shape when
subjected to a force. In the following, we will assume that the objects we are dealing with are
rigid bodies. The physics describing
Vectors
y
y2
A
A! cos
! x2 x1 Ax
A=
= !
=
A
y
y
2 1 y A sin
!
Ax and Ay are components of vector A .
Ay
y1
Ax
x1
!
A ,
Ax , Ay
Ax , Ay
!
A ,
x2 x
From trigonometry:
Magnitude:
A
cos = !x
A
!
Ax = A cos
A
sin = !y
A
!
Ay = A sin
!
A = Ax2 + Ay2
Simple Harmonic Motion
The Physical Pendulum
Calculate the torque due to the weight of the rotating
object with respect to the pivot (rotation axis):
!
! !
!
= r F = d mg = d m gsin
pivot
(rotation axis
perpendicular
to the page)
y
d
From Newtons 2nd La
Fluid Dynamics
Pressure
The density of a substance is defined as its mass per unit volume:
=
m
V
The pressure P is defined as force per unit area, where the force F is understood to be the
magnitude of the force acting perpendicular to the surface area A:
Circular Motion
When an object is moving on a circular track at a constant
speed, we say that the object is performing uniform
circular motion. Because, although the speed is constant,
the velocity of the object is not constant it keeps changing
direction
Thermodynamics
Useful Unit Conversions
Measuring temperature:
(TF 32 F )
Fahrenheit Celsius
TC =
Celsius Kelvin
TK = TC + 273.15K
5
9
where TC, TF, and TK are the temperature in Celsius, Fahrenheit, and Kelvin, respectively. The
S.I. unit for temperature
y
Work and Energy
F
F
It changes direction
of motion
but not speed
F
It changes speed but
not direction of motion
v
Work
x
!
From observation, you can infer that to change the
! speed the magnitude! of v of an object,
the most
is to apply a force F parall
Impulse and Momentum
Impulse and Linear Momentum
!
If a constant force F acts on an object during a time interval t , the velocity of the object will
! !
change from vi to vf . The acceleration of the object will be:
! ! !
! v vf vi
a=
=
t
t
From Newtons
1.1 Problem with Vectors #1
Calculate magnitude and direction for the following vectors:
s-a=<:>
[5]. < sMsr. 585/
(,3 a x tut We 49-02974 % (5-49.210 many.
6*
PMC HWII
Y ,
cfw_9 X +an91IEg 3% : 309; % ):/+ I800: Zlo-W/
1.2 Problem with Vectors #2
Find th
Homework 6
Due Monday, October 5, 2015, in recitation
Problem with Energy, and more than one Body #1
H
m2 = 2kg
H2 = 0.4m
m3 = 1.5kg
H1 = 0m
m1 = 6kg
In the figure on the left hand side, the
strings and the pulleys are massless,
and there is no friction e