PHY 2049 Test 1 Flashcards
Length (L) SI unit
meter (m)
Mass (M) SI unit
kilogram (kg)
Time (T) SI unit
second (s)
Electric Current (A) SI unit
ampere (A)
Absolute Temperature (theta) SI unit
kelvin (K)
Luminous Intensity (I) SI unit
candela (cd)
Amount of substance (n) SI unit
mole (mol)
Tera-
10^12
Giga-
10^9
Mega-
10^6
Kilo-
10^3
Hecto-
10^2
Deca-
10^1
Deci-
10^ -1
Centi-
10^ -2
Milli-
10^ -3
Micro-
10^ -6
Nano-
10^ -9
Pico-
10-12
Reduces long numbers to manageable width
Scientific Notation
Size of a number is adjusted by changing the
Magnitude (x 10^?)
Any meaningful equation must have the same dimensions in the
Left and Right sides
Things being added must have
The same dimensions
Exponents and trig arguments must be
dimensionless
The pressure in fluid motion depends on its
Density and Speed
P=
M/LT^2
Density (p) = M/L^3
Speed (v) = L/T
P/density = speed^2
Area
A = L^2
Volume
V=L^3
Speed
v=L/T
Acceleration
a=L/T^2
Force
F=ML/T^2
Pressure (F/A)
p = M/LT^2
Density (M/V)
p=M/L^3
Energy
E=ML^2/T^2
Power (E/T)
P=ML^2/T^3
Figure that is reliably known
Significant figure
All non-zero digits are
significant
Zeros are significant when…
- Between other non-zero digits
- After the decimal point AND another significant figure
- Can be clarified by using scientific notation
Number of significant figures
Accuracy
When multiplying or dividing (significant figures)
Round the result to the same accuracy as the least accurate measurement
Ex. 4.5 X 7.3 = 32.85 = 33 (2 sig figs)
When adding or subtracting (significant figures)
Round the result to the smallest number of decimal places of any term in the sum
Ex. 135 + 6.213 = 141.213 = 141 (3 sig figs)
A quantity that has both magnitude and direction
Vector
Vectors are represented graphically as
Arrows: directed lines with arrowheads at their ends
Row or column vectors are represented as
i for x, j for y, k for z
Specify which position in a row or column vector that the accompanying number should go
i, j, and k
Unit vectors in the x, y, and z directions
i, j, and k
Said to have a length of 1
Unit vectors are to have a length of
1
Magnitude of a vector is calculated by:
[v] = (sq. rt. (vx^2 + vy^2 + vz^2))
The direction of a 2-dimensional vector can be specified by the angle it makes with
The positive x-axis
Theta = tan^-1 (vy/vx)
Theta = cos^-1(vx/[v])
Theta = sin^-1 (vy/[v]
Given magnitude and direction the components of a vector can be recovered by
vx=[v]cos theta
vy=[v]sin theta
Vector A + Vector B =
Vector C
Vector Ax + Vector Ay =
Vector A
Vector A = - Vector B if
[Vector B] = [Vector A] and their directions are opposite
Vector B = s Vector A has manitude
[B] = [s][A] and has the same direction as A if s is positive or - [A] if s is negative
Slide 18
Comeback to
Displacement
Slide 19
Vector = x i + y j [v] = (sq. rt (x^2 + y^2)) Theta = (tan^-1 ([v]) vx = v cos theta vy = v sin theta
Slide 21
comeback to
Defined in terms of a set of coordinates or frame of reference
Position
In one dimension this is either the x- or y-axis
Position or Frame of reference
Measures the change in position
Displacement
A vector quantity
Represented as delta x (if horizontal) or delta y (if vertical
Displacement
A vector quantity
Displacement units
SI: Meters (m)
CGS: Centimeters (cm)
USCS: Feet (ft)
Curvy line over straight line
Straight line = Displacement
Curvy line = Distance
Distance may be, but is not necessarily, the
Magnitude of the displacement
The rate at which the displacement occurs
Average velocity
Velocity (average) =
delta vector x/ delta t
Delta t is always
positive
Average velocity is a
Vector
Direction will be the same as the direction of the displacement
The limit of the average velocity as the time interval becomes infinitesimally short, or as the time interval approaches zero
Instantaneous velocity
Velocity (instantaneous) =
Lim (delta t –> 0) delta vector x/ delta t
Indicates what is happening at every point of time
Instantaneous velocity
Slope of the tangent to the curve at the time of interest
Instantaneous Velocity
The magnitude of the instantaneous velocity
Instantaneous speed
Changing velocity (non-uniform) means
An acceleration is present
The rate of change of the velocity
Average acceleration
Acceleration (average) =
Delta vector v(velocity)/delta t
Average accelerations is a
Vector quantity
The limit of the average acceleration as the time interval goes to zero
Instantaneous Acceleration
Acceleration (instantaneous) =
Lim (delta t –> 0) delta v/delta t
When the instantaneous accelerations are always the same, the acceleration will be
uniform
The instantaneous accelerations will all be equal to the average acceleration
The slope of the line connecting the initial and final velocities on a velocity-time graph
Average acceleration
The slope of the tangent to the curve of the velocity-time graph
Instantaneous acceleration
Slide 29
Comeback to picture
Velocity as a function of time
v=v0 + at
Displacement as a function of velocity and time
delta x = 1/2 (v0 + v)t
Displacement as a function of time
delta x = v0t + 1/2 at^2
Velocity as a function of displacement
v^2 = v0^2 + 2a delta x
Motion is along the ___ axis
X
At t=0 the velocity of the particle is
v0
All objects moving under the influence of only gravity are said to be in
Free fall
All objects falling near the earth’s surface fall with a
Constant acceleration
The constant acceleration of objects falling near the earth’s surface is called
Acceleration due to gravity and is indicated by g
For constant acceleration, two of the equations of motion can be easily derived using
Integration
dv/dt = a (integrate it)
Slide 32, 33
comeback to
The position of an object is described by
Its position vector, r
The change in an object’s position
Displacement
delta r = r (final) - r (initial)
The ration of the displacement to the time interval for the displacement
The average velocity
v (avg) = delta r/ delta t
The limit of the average velocity as delta t approaches zero
The instantaneous velocity
v= lim (delta t –>0) delta r/delta t
An extended object whose parts are at rest relative to each other
Frame of reference
To make position measurements we use
Coordinate axis that are attached to reference frames
If a particle moves with velocity Vpc relative to reference frame C, which is in turn moving with velocity Vcg relative to reference frame G, the velocity of the particle relative to G is:
VpG = VpC + VCG
This is called the Galilean transformation equation **
The rate at which velocity changes
Average acceleration
a (avg) = delta v/delta t
The limit of the average acceleration as delta t approaches zero
Instantaneous acceleration
a = lim (delta t –> 0) delta v/delta t
Ways an object might accelerate
- The magnitude of the velocity can change
- The direction of the velocity can change (even though magnitude is constant)
- Both can change
No x or x0
v(t) = v0 + at
No v(t)
delta x(t) = v0t + 1/2 at^2
No t
v^2(t) = v0^2 + 2a(x-x0)
No a
Delta x(t) = 1/2 (vo+v(t))t
No v0
Delta x(t) = v(t)t - 1/2 at^2
Slide 40
Come back to
When an object moves in both the x and y direction simultaneously under the influence of a constant gravitational force, the form of two dimensional motion that results is called
Projectile motion
Using our assumptions, an object in projectile motion will
Follow a parabolic path
The velocity of the projectile at any point of its motion is the
Vector sum of its x and y components at that point
Polar and rectangular vector representations are
related
Slide 43
X-direction of Projectile Motion
ax = 0
Vxo=V0 cos theta0 = Vx = constant
x = Vxo t
This is the operative equation in the x-direction since there is uniform velocity in that direction
Y-direction of Projectile Motion
Vyo = V0 sine theta0
Take the positive direction as upward
Then: free fall problem only then: ay = -g
Uniformly accelerated motion, so the one dimensional motion equations all hold
Slide 46, 47, 48, 49, 50
Come back to
A particle moving in a circle with varying speed has
Tangential acceleration
a of t = dv/dt
Tangential acceleration is in addition to
The radial, centripetal acceleration
a of c = v^2/r
a = (sq. rt. (a of c ^2 + a of t^2))
Newton’s first law
Body at rest remains at rest
Body in motion stays in motion unless acted upon by an unbalanced EXTERNAL force
The property of a body that causes it to remain at rest or maintain constant velocity is called its
Inertia or mass
Mass is a
Scalar quantity
Units of mass
SI: Kilograms (kg)
CGS: grams (g)
US Customary: slug (slug) or lbm (pound-mass)
1 kg =
1000g = 2.2 lbm
1 slug =
32.2 lbm
Newton’s second law
The acceleration produced by forces acting on a body is directly proportional to and in the same direction as the net external for and inversely proportional to the mass of the body.
F= ma
The acceleration produced by forces acting on a body is directly proportional to and in the same direction as the net external for and inversely proportional to the mass of the body.
Newton’s second law
Body at rest stays at rest….
Newton’s first law
Both F and a in the equation F= m/a are
Vectors
All the internal forces in a body, such as the forces between atoms and molecules in it, can be completely ignored because
They do not contribute to acceleration of the object as a whole
The magnitude of the gravitational force acting on an object of mass near the earth’s surface is called the
Weight (w) of the object
w = mg
Special case of Newton’s second law
w = mg
g can also be found from the
Law of Universal Gravitation
The pound (lb) in the USCS system is ambiguous as whether is measures
Mass or force
We define the pound-mass as
0.4536 kg
We define the pound-force as
4.45N
Pound-mass and pound-force are related through
w = mg
See slide 55
Another lb related unit
The poundal
1 pdl = 1 lbm x ft/s^2
1 lbf = 32.2 pdl
F (gravity) =
w = mg
Force units
SI: N
USCS: pdl, lbf
Mass units
SI: kg
USCS: slug, lbm
Types of fundamental forces
- Strong nuclear force (strongest)
- Electromagnetic force
- Weak nuclear force
- Gravity (weakest)
Characteristics of fundamental forces
- All field forces
2. Only gravity and electromagnetic in mechanics
Other classes of forces include
Cohesion, adhesion, thrust, drag, friction, lift and shearing force
All of these are based on the electromagnetic interactions between the atoms of various substances
According to current understanding there are
4 forces in nature
Two of these operate in the nucleus
All common and familiar forces are either gravitational or electromagnetic in origin
Perpendicular to direction of the surface of contact
Normal contact force
Forces parallel to surface of contact
Friction
The force of springs follows
Hooke’s Law
F = -kx
A special diagram showing only the forces acting on a body
Free body diagram
Free body diagram
- Identify all the forces acting on the object of interest
- Choose an appropriate coordinate system
- Represent the body as a point and draw the forces in appropriate directions
Slide 60
Applying Newton’s Laws
- Make a sketch
- Draw free body diagram
- Assign forces to x and y components
- Apply F = ma and keep track of signs
- If more than one object, apply Newton’s third law
- Solve
If there is more than one object
Apply Newton’s 3rd law
Whenever one body exerts a force on a second body, the second body exerts a force back on the first that is equal in magnitude and opposite in direction
Newton’s 3rd Law
For every action there is an equal and opposite reaction
Newton’s third law
For every action, there is an equal and opposite reaction
