Chapter 1 Kinematics and Dynamics Flashcards
Force equation
Newton (Kg x m)/s^2
Work and energy
Joule (kg x m^2)/s^2
Power
watt (kg x m^2)/s^3
1 nanometer = how many meters
1 nm = 10^-9 m
1 eV = how many joules
1 eV = 1.6 x 10^-19 J
What is a vector
- magnitude and direction
- displacement, velocity, acceleration, force
What is a scalar
- numbers that have magnitude only, no direction
- distance, speed, energy, pressure, mass
resultant
- sum/difference of two or more vectors
tip-to-tail method
- used when finding the resultant of two vectors…
ex: vectors A and B… place the tail of B at the tip of A without changing either the length or direction of either arrow - lengths of arrows are proportional to magnitudes of vectors
x and y method
- break vector into perpendicular components
- horizontal and vertical
Draw x and y method example + equations
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how can you find the magnitude of V if X and Y are given
- use pythagorean theorem
pythagorean theorem
X^2 + Y^2 = V^2
Steps to find resultant using the components method:
- resolve vectors to be added into their x and y components
- add the x components to get the x-component of the resultant. Do the same for Y
- Find the magnitude of the resultant by using the pythagorean theorem
- Find the direction (theta) of resultant by using the tan relationship
Vector subtraction
- add a vector with equal magnitude, but opposite direction, to first vector
- A - B = A + (-B)
- -B represents vector with same magnitude as B, in opposite direction
Vector multiplication by a scalar
- magnitude of vector changes by multiplied by a scalar
- ex: vector A x scalar value n creates vector B
- B = nA
- find magnitude of B… multiply magnitude of A by absolute of n
- n = +, same direction
- n = - , opposite direction
To generate scalar quantity of work
- multiply magnitudes of two vectors of interest (force and displacement) and the cosine of the angle between the two vectors
- known as the dot product ( A * B)
To generate a third vector like torque
- generating a third vector like torque, determine magnitude and direction
- multiply the magnitudes of the two vectors of interest (force and lever arm) and the sine of the angle between the two vectors
- use the right hand rule to determine its direction
- known as the cross product ( A x B)
How to determine the cross product resultant vector
- right hand rule
- ex: C = A X B
practice this rule - point thumb in direction of vector A
- extend fingers in direction of vector B
- palm establishes the plane between the two vectors… direction of palm pointing = direction of resultant C
Velocity
- vector…
- magnitude measured as the rate of change of displacement in a given unit of time, m/s
- v = x/t
speed
- rate of actual distance traveled in a given unit of time
Force definition
- vector quantity that is experiences as pushing or pulling on objects
Gravitational force
Fg = Gm1m2 / r^2
- G = gravitational constant
(6.67 x 10^-11 )(N * m^2) / kg^2))
- m1,m2 = masses of two objects
- r = distance between their centers of mass
Mass of a proton
1.67 x 10^-27 kg
mass of an electron
9.11 x 10^-31 kg
Static friction
- exist between stationary object and the surface upon which it rests
Kinetic friction
- sliding object and the surface over which the object slides
How to measure magnitude of kinetic friction
fk = uk x N
uk = coefficient of kinetic friction
N = normal force
mass and weight relationship
Fg = mg
Fg = weight of the object
m = mass
g = acceleration due to gravity (9.8)
center of mass equation
x = (m1x1 + m2x2 + m3x3…) / m1+m2+m3
repeat for y and z…
- m1,m2,m3 are three sample masses
- x,y,z = coordinates
Acceleration
- rate of change of velocity that an object experiences are the result of a force
- v/t
Newtons first law
Fnet = ma = 0
- Fnet is the net force, m is the mass and a is the acceleration
- a body either at rest or in motion with constant velocity will remain that way unless a net force acts. upon it (law of inertia)
Newtons second law
Fnet = ma
- object of mass m will accelerate when the vector sum of the forces results in some nonzero resultant force vector
Newtons third law
- F_AB = - F_BA
- to every action there is an opposed but equal reaction
Linear motion
- objects velocity and acceleration along same line of motion so the pathway of the moving object continues along a straight line
Equations for falling objects exhibiting linear motion with constant acceleration:
- v = v0 +at
- x = v0t +((at^2)/2)
- v^2 = v0^2 + 2ax
- x= v(line)t
x, displacement… v, velocity… a, acceleration…
Air resistance
- value increases as speed of the object increases
- object in free fall will experience drag force
- drag force will become equal in magnitude to the weight of the object, and object will fall with constant velocity (terminal velocity)
Projectile motion
- follows a path along two dimensions
- Vy changes at the rate of g, Vx will remain constant
Inclined planed
- divide force vectors into components that are parallel and perpendicular
- Fg, II = mg sin
- Fg, I = mg cos
Fg, II is component of gravity parallel to the plane (orients down the plane)
Fg, I is the component of gravity perpendicular to the plane (oriented into the plane)
Circular motion
- instantaneous velocity vector is always tangent to the circular path
- Fc = mv^2 / r
- Fc is magnitude of centripetal force…. m is the mass… v is the speed… r is the radius of the circular path
translational equilibrium
- exists only when the vector sum of all of the forces acting on an object is zero
- will have constant speed and constant direction
Equation for torque
- cross product
- torque = r x F = rF sin theta
r = length of lever arm, f = magnitude of the force, theta = angle between lever arm and force vectors
