Exam 2
what is kinetic energy dependent on?
mass and velocity
what is linear momentum dependent on?
mass and velocity
equation for linear momentum
mass x velocity
dependents of PE
mass, gravity (weight) and height
KE = will always be a ______ number
positive
Energy transferred to the object is ___________ work, and energy transferred from the object is _______________ work.
positive negative
definition of average power?
rate at which work is done P = W/t (work/time ... so the change in energy over time)
important information to review for banking on a curve?
requires centripetal force to keep it moving in a circular path - weight (mg) is straight down, Normal force is straight up with reference to the car (giving it components)
When a net force acts on an object, the impulse of the net force is =
to the change in momentum of the object.
equation for velocity of motion...
v = 2pi*r / T
what is centripetal acceleration dependent on?
velocity and the radius
potential energy relation with work...
w = PE initial - PE final
steps to finding the equation for Fc?
Fnet = ma Fc = mAc Fc = mv^2 / r (Ac = V^2 / r)
Wnc = what in conservation of mechanical energy
Wnc = (KEf + PEf) - (KEo + PE0) so Wnc = Ef - Eo
who equation written out for Wnc =
Wnc = 0.5mvf^2 - 0.5mvo^2 + mghf - mgho
equation for Wnc?
Wnc = change in KE + change in PE
conservative forces = nonconservative forces =
(independent) - gravitational forces - elastic spring force - electric force (dependent) - static and kinetic frictional forces - air resistance - tension - normal force - propulsion force of a rocket
W = (Fcostheta) s W(gravity = (_________)*(_______________)
(mg) * (ho - hf) fcos s
what are 3 examples of a conservative force?
- gravitational force (Fg, is in our PE equation (mg)) - Elastic spring force - Electric force
when looking at Velocity & Centripetal Acceleration which way do they point in a example?
- the acceleration vector always points towards the center - the velocity vector is always tangent to the path (meaning that velocity and acceleration are perpendicular to one another)
However, when F is perpendicular to s: W = ?
0 (example = pushing box horizontally and then someone picks it up vertically, work done = 0, because goal was in the X and was removed)
1 Newton =
1 kg m/s^2
1 joule =
1 kg m^2/s^2 = 1 N * m
steps to solve for the banking angle equation...
1. FnSIN(theta) = mv^2 / r 2. FnCOS(theta) = mg (combine)... FnSIN(theta)/FnCOS(theta) = mv^2 / r(mg) (cancel) 3. Sin(theta)/Cos(theta) = v^2/gr 4. tan(theta) = v^2/gr
important things to remember for this chapter from previous units?
Fnet = ma and how to sum up forces + use Pythagorean theorem and trig identities.
what doe 2pi*r represent?
2pi*r (circumference of the circle)- is the distance traveled.
equation for the time of the particle to complete (1) full circle (one revolution) is...
2pi*r / V
1 horsepower = what = how many watts?
= 550 ft *lbs /s = 745.7 watts
a force is conservative if...
A force is conservative if the work it does on an object moving between two points is *independent* of the path the object takes between the points. (don't care what happens in between, a example, would be dropping a pen on a table, can get to point A and b)
define a nonconservative force?
A force is nonconservative if the work it does on an object moving between two points *depends* on the path taken. (DOES WORK, has forces acting on object)
define linear momentum...
A measure of the motion of an object & is = to the product of the object's mass & its velocity (at a constant velocity)
equation for centripetal acceleration...
Ac = v^2 / R Here v is the speed of the particle and r is the radius of the circle.
what is important to note about acceleration?
As the direction of the velocity of the particle changes, there is an acceleration!!!
Fc = ?
Fg (don't think is right)
equation to determine the total amount of energy?
E = KE + PE
equation for the conservation of energy?
E0 = Ef KEo + PEo = KEf + PEf
what is the principle of conservation of energy?
Energy can neither be created not destroyed, but can only be converted from one form to another. (nothing gained and nothing is lost)
simplified definition of energy
Energy is defined as the ability to do work
equation for the impulse momentum theorem...
F*t = mvf - mvo
Fg = (steps to get satellite velocity)
Fc so... Fc = Mv^2 /r and Fg = Gm1M2/r^2 GMe*m/r^2 = Mv^2/r V^2 = GMe/r (square root) V = square root of GMe/r
centripetal force abbreviation
Fc (means moving in a circular path)
what two factors point toward the center of a circle?
Force and Acceleration
what are the equations for friction?
Fs = Us * N Fk = Uk * N
why do we study circular orbit? give a real life example as to why?
GPS, uses radio waves from multiple satellites to pinpoint a location.
define impulse
Impulse is the product of the average force combined with the time interval during which the force acts
in normal situations how do conservative and nonconservative forces act on one another?
In normal situations both conservative and nonconservative forces act simultaneously on an object, so the work done by the net external force can be written as --> Wtotal = Wc + Wnc
conservative force depends on what?
It depends only on the initial & final positions of the object. (so if have a ball dropped straight down vs, a ball thrown a cure, both will have the same initial and final height do not care that the one ball moved horizontally)
equation for impulse
J=F(ave)t units = N * s or kg m/s
units for work
Joules = 1N*m
equation for KE?
KE = 1/2mv^2 (KE units = J)
what is Kinetic energy?
Kinetic energy, KE is energy associated with the state of motion of an object. The faster the object moves, the greater is its kinetic energy.
(chp. 7 - impulse and momentum) what represents linear momentum?
P (is a vector)
Gravitational Potential Energy =
PE (in the vertical)
equation for Potential energy
PE=mgh
define PE (potential energy)
Potential energy, PE is energy that an object has due to its position in space
steps to getting PE = mgh
S = ho - hf W = fcos0(s) = 1 W = fs W = fgs (fg = w = mg) W = mgs W = mgh
equation for the period of a satellite...
T = 2pi*r^(3/2) / square root of G*Me
definition of gravitational potential energy
The gravitational potential energy PE is the energy that an object of mass m has by virtue of its position relative to the surface of the Earth. That position is measured by the height h of the object relative to an arbitrary zero level: PE = mgh
(chp. 5 - uniform circular motion) ______________ + ___________________ = uniform circular motion
The speed of the particle is constant + A particle travels around a circle/circular arc
what is the principle of conservation of mechanical energy...
The total mechanical energy (E = KE + PE) of an object remains constant as the object moves, provided that the net work done by external nonconservative forces is zero. (0 = KE + PE)
when is the impulse momentum theorem used?
There are many situations when the force on an object is not constant.
equation for Velocity of the satellite in circular orbit...
V = square root of G*Me/r
equation when force is exerted at some angle?
W = (Fcos(theta))s Cos (0) = 1 Cos (90) = 0 Cos (180) = -1
how does W relate to KE?
W = KEf - KE0
W = w =
W = Watt w = weight
Fg =
W = mg
Work, is what? (define)
W is energy transferred to or from an object by means of a force acting on the object.
units of average power...
Watt (W) = j/s
Impulse is defined as?
a change in motion leads to a change in velocity - is a vector (J)
A centripetal force accelerates a body by...
by changing the direction of the body's velocity without changing the body's speed
in many situations such as a bullet hitting a carrot, we cannot use newtons 2nd law to solve problems because we know very little about what?
about the complicated forces involved (this is what this chapter teaches us more about)
Since the speed v here in centripetal force is constant, the magnitudes of the _________ and the __________ are also constant.
acceleration and the force
2 examples of nonconservative forces?
air resistance and friction (affect motion)
important note of the relationship between momentum and velocity?
always in the same direction (if one is up the other is up
describe the amount of PE and KE on the way down a hill?
at the top before start have all the potential energy as you go down the PE gets converted into KE. As you loose height there is a decrease in PE but you gain KE
when moving in a circular path we are accelerating because why?
because we are always changing its direction
Centripetal means what?
center seeking
equation for velocity
distance / time
what is important to note about the work equation?
force and displacement need to be in the same direction
definition of the impulse momentum theroum?
impulse = to the change in momentum
units for velocity of motion...
m/s
what stays the same in the initial and final KE?
mass
w = ?
mg and N = W (when acceleration is 0, f = ma, so N - W = 0)
important to note about the radius?
needs to be center to center!!!!
T is called the...
period of revolution or period of the motion. (one whole circular path)
FN =
perpendicular to the surface
equation for work when F and S are in the same direction and when they are in the opposite direction (think of guy pressing)
same direction (parallel)... W = (F cos 0)s = Fs Opp. Direction... W = (F cos 180) s = -Fs
(chp. 6 - Work and Energy) is work a vector or a scalar?
scalar (does not convey direction)
how get the KE equation?
start with W = Fs and F = ma so, W = mas (and Vf^2 = Vo^2 + 2ax (x = s), solve for as) W = m (Vf^2 - Vo^2/2 / 2) and take 2 out and make 0.5 and add m in get final KE - initial KE = work how get equation
how do we get the equation for Wnc...
start with W = change in KE and W = Wc + Wnc add together and know change in KE, but what is Wc Wc = Wg = mgho - mghf (input in) (only conservative force acting is gravitational force) solve for Wnc and that is how you get.
steps to the impulse-linear momentum theorem...
start with newtons second law f = ma and acceleration = change in velocity / change in time - add equations together - factor in mass into the change in velocity - multiply time to the other side - get impulse = to the change in momentum (on slides 8 - 10)
Equation to solve for: the banking angle
tan(theta) = V^2 /gr also rewritten as theta = tan-1 (V^2/gr)
The net force causing the centripetal acceleration is called
the centripetal force, Fc - & points in the same direction as the acceleration, toward the center of the circle.
definition for work...
the magnitude of the force applied to an object times the distance the object moves in the *direction of the force.*
side note the faster and larger the mass the ______________ KE?
the more KE we will have, because will cause more damage
Period of the satellite is the ...
time required for one orbital revolution
what is banking of a curve used for?
to stop skidding (race tracks have this)
what is T?
the period in seconds that it takes for one circular path
Equation for work? (done by a constant force)
work (J) = force (N) x displacement (m)
