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Physics and Math Correct Deck > Ch. 1: Kinematics and Dynamics > Flashcards

Ch. 1: Kinematics and Dynamics Flashcards

1
Q

what are the 7 SI units and the corresponding “thing” that they measure?

A
  1. METER –> length
  2. KILOGRAM –> mass
  3. SECOND –> time
  4. AMPERE –> current
  5. MOLE –> amount of substance
  6. KELVIN –> temperature
  7. CANDELA –> luminous intensity
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2
Q

defn: base unit vs. derived unit

A

BASE UNIT = the standard units around which the system itself is designed

DERIVED UNIT = created by associating base units with each other (i.e. a Newton)

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3
Q

what is an angstrom in terms of meters?

A

1 A = 10^-10 m

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4
Q

what is a nanometer in terms of meters?

A

1 nm = 10^-9 m

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5
Q

what is an electron-volt in terms of Joules? what does an eV represent?

A

1 eV = 1.6 x 10^-19 J

the amount of energy gained by an electron accelerating through a potential difference of one volt

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6
Q

defn: vectors (4 examples) vs. scalars (5 examples)

A

VECTOR = numbers that have magnitude and direction
1. displacement 2. velocity 3. acceleration 4. force

SCALAR = numbers that have magnitude only, not direction
1. distance 2. speed 3. energy 4. pressure 5. mass

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7
Q

defn: resultant

A

the sum or difference of two or more vectors

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8
Q

defn + process: tip to tail method

A

one method of finding the resultant of two vectors

place the tail of B at the tip of A without changing the length or direction of either arrow

the lengths of the arrows must be proportional to the magnitudes of the vectors

the vector sum of A + B is the vector joining the tail of A to the tip of B and pointing toward the tip of B

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9
Q

defn: component method of vector addition

A

break each vector into perpendicular components (most often x and y), however in some circumstances it makes more sense to define them as parallel and perpendicular to some other surface

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10
Q

what is a simple way of describing the x and y components of a resultant vector?

A

the x component is the sum of the x components of the vectors being added

the y component is the sum of the y components of the vectors being added

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11
Q

how do you subtract one vector from another? what does this look like mathematically?

A

by adding a vector with equal magnitude but opposite direction to the first vector

A - B = A + (-B) where -B represents a vector with the same magnitude as B but pointing in the opposite direction

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12
Q

how does the component method work for vector subtraction?

A

the x-component of the resultant vector is the difference of the x-components of the vectors being subtracted

the y-component of the resultant vector is the difference of the y-components of the vectors being substracted

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13
Q

what is the result of a vector A being multiplied by a scalar n (magnitude and direction)?

A

new vector B = nA

magnitude: |n|A

direction: look at the sign of n
- if n is positive: B and A are in the same direction
- if n is negative: B and A point in opposite directions

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14
Q

defn + equation: dot product

does this generate a vector or scalar product?

A

the dot product is how we multiply vectors by other vectors

SCALAR product: A dot B = |A| |B| cos theta

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15
Q

defn + equation: cross product

does this generate a vector or scalar product?

A

the cross product is another way of how we multiply vectors by other vectors

VECTOR product: A x B = |A| |B| sin theta

once we have the magnitude we use the right-hand rule to determine its direction

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16
Q

what direction is the resultant of a cross product in relation to the plane created by the two vectors? what does this mean physically on the MCAT?

A

resultant of a cross product will ALWAYS BE PERPENDICULAR to the plane created by the two vectors

on the MCAT: usually means the vector of interest is going into or out of the screen

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17
Q

what are the three steps of applying the right hand rule when considering a resultant C where C = A x B?

A
  1. Point your thumb in direction of vector A
  2. Extend your fingers in the direction of vector B (you may need to rotate your wrist to get the correct configuration)
  3. Your palm establishes the plane between the two vectors –> the direction your palm points is the direction of the resultant C
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18
Q

what is a secondary method (not the palm method) of using the right hand rule for a resultant C = A x B?

A
  1. Point the right index finger in the direction of A
  2. Point the right middle finger in the direction of B
  3. Hold the thumb perpendicular to these two fingers, it is the direction of C
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19
Q

defn: displacement (x or d)

is this a vector or scalar quantity?

A

displacement = an object in motion may experience a change in its position in space

this is a vector quantity (has both magnitude and direction)

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20
Q

what does the displacement vector connect?

A

the object’s initial and final position

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21
Q

does displacement consider the path?

A

NO! only the net change in position from initial to final

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22
Q

defn: distance

how does this differ from displacement?

A

a scalar quantity that considers the pathway taken

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23
Q

magnitude + SI unit + direction: velocity

A

magnitude: the rate of change of displacement in a given unit of time

SI units: meters/second

direction: the same direction of the displacement vector

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24
Q

defn: speed

A

the rate of actual distance traveled in a given unit of time

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25
Q

what is the relationship between an object’s instantaneous speed and an object’s instantaneous velocity?

A

the instantaneous speed of an object will always be equal to the magnitude of the object’s instantaneous velocity

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26
Q

defn: instantaneous velocity

A

a measure of the average velocity as the change in time (delta t) approaches zero

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27
Q

defn: average speed vs. average velocity

A

average SPEED = a measure of distance traveled in a given period of time

average VELOCITY = a measure of the displacement of an object over a given period of time

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28
Q

every change in velocity is motivated by a what?

A

a push or a pull (a force

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29
Q

defn + SI unit: Force (F)

A

a vector quantity that is experienced as pushing or pulling on objects (they do not need to touch!)

SI unit: newton (N) = kg.m/s^2

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30
Q

defn: gravity

A

an attractive force that is felt by all forms of matter

all objects exert gravitational forces on each other (no matter how small!)

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31
Q

why do gravitational forces usually not have much significance on a small scale?

A

other forces tend to be much larger in magnitude

they only really take on a significant value on the planetary level

32
Q

defn: friction

A

a type of force that opposes the movement of objects and cause it to slow down or become stationary

33
Q

what are the two types of friction?

A

static

kinetic

34
Q

defn: static friction (fs)

A

exists between a stationary object and the surface upon which it rests

35
Q

defn: coefficient of static friction (us)

A

a unitless quantity that is dependent on the two materials in contact

36
Q

defn: normal force

A

the component of the force between two objects in contact that is perpendicular to the plane of contact between the object and the surface upon which it rests

37
Q

what does it mean when static friction = 0?

A

an object is resting on a surface with no applied forces

38
Q

if an object is stationary, is it necessarily experiencing a maximal static force of friction?

A

no

39
Q

what will any applied force below the threshold of the maximal value of static friction to the the object?

A

it will not be sufficient to move the object as there will be an equal but opposite force of static friction opposing the object’s motion

40
Q

defn: kinetic friction (fk)

A

exists between a sliding object and the surface over which the object slides

any time two surfaces slide against each other, there will be kinetic friction present

41
Q

what are the two main distinctions between the equations for static and kinetic friction and what do these differences imply?

A

KINETIC FRICTION EQUATION HAS AN EQUALS SIGN –> kinetic friction will have a constant value for any given combination of a coefficient of kinetic friction and normal force

DIFFERENT COEFFICIENTS OF FRICTION –> us is always larger than uk (the max value for static friction will always be greater than the constant value for kinetic friction –> objects will stick until they stat moving and then will slide more easily over each other)

42
Q

does the amount of surface area in contact or the velocity of the sliding object affect the value of kinetic friction?

A

no! the value of kinetic friction is a constant for any given combo of a coefficient of kinetic friction and normal force

43
Q

defn: mass vs. weight

+ (scalar vs. vector, SI unit)

A

mass (m) = a measure of a body’s inertia = the amount of matter in the object

  • scalar
  • SI unit: kilogram

weight (Fg) = a measure of the gravitational force (usually of Earth) on an object’s math

  • vector
  • unit: newtons (N)
44
Q

defn: center of mass or gravity

A

the weight of an object can be though of as being applied at a single point in that object

45
Q

defn: acceleration (a)

vector or scalar?
SI units?

A

the rate of change of velocity that an object experiences as a result of some applied force

vector
Si units: meters/s^2

46
Q

defn: deceleration

A

acceleration in the direction opposite the initial velocity

47
Q

on the graph of velocity vs. time, what is the tangent to the graph at any time t (the slope of the graph at that time)

A

the instantaneous acceleration

48
Q

Newton’s first law

A

Fnet = ma = 0

where Fnet = net force, m = mass, a = acceleration

A body either at rest or in motion with constant velocity will remain that way unless a net force acts upon it (the law of inertia)

49
Q

Newton’s second law

A

Fnet = ma

An object of mass m will accelerate when the vector sum of the forces results in some nonzero resultant force vector

note: the net force and acceleration vectors necessarily point in the same direction

50
Q

Newton’s third law

A

FAB = - FBA

the law of action and reaction

To every action, there is always an opposed but equal reaction

More formally: for every force exerted by object A on object B, there is an equal but opposite force exerted by object B on object A

remember: physical contact is not necessary

51
Q

defn: linear motion

A

the object’s velocity and acceleration are along the line of motion, so the pathway of the moving object continues along a straight line

52
Q

value: acceleration due to gravity

A

g = 9.8 m/s^2

53
Q

defn: free fall

A

an object would fall with constant acceleration (g) and would not reach terminal velocity

54
Q

char: air resistance (2)

A
  1. opposes the motion of an object
  2. its value increases as the speed of the object increases
55
Q

proc: drag force

A

an object in free fall will experience a growing drag force as the magnitude of its velocity increases

56
Q

defn: terminal velocity

A

eventually, the drag force will be equal in magnitude to the weight of the object and the object will fall with constant velocity according to Newton’s first law

57
Q

defn + char: projectile motion

A

motion that follows a path along two dimensions

the velocities and accelerations in the two directions are INDEPENDENT of each other and must be analyzed separately

58
Q

for projectile motion, is the acceleration of gravity felt in the vertical direction? in the horizontal direction?

what does this imply

A

ONLY in the vertical direction

that only means that vy will change at the rate of g but vx will remain constant

59
Q

why can we generally assume that horizontal velocity in freefall is 0 on the MCAT?

A

we usually assume that air resistance is negligible and thus no measurable force is acting along the x-axis

60
Q

approach: inclined planes

A

divide force vectors into components that are parallel and perpendicular to the plane

most often, gravity must be split into components

Fg parallel = mg sin theta –> the component of gravity parallel to the plane (oriented down the plane)

Fg perpendicular = mg cos theta –> the component of gravity perpendicular to the plane (oriented into the plane)

61
Q

defn: circular motion

A

occurs when forces cause an object to move in a circular pathway

upon completion of one cycle, the displacement of the object is zero

62
Q

char (6): uniform circular motion (traditional focus on MCAT)

A
  1. speed of the object is constant
  2. the instantaneous velocity vector is always tangent to the circular path
  3. the object moving in the circular path has a tendency (inertia) to break out of its circular pathway and move in a linear direction along the tangent
  4. it is kept from doing so by a centripetal force (always points radially inward)
  5. we can resolve the forces into radial and tangential components
  6. the tangential force is zero because there is no change in the speed of the object
63
Q

defn: centripetal acceleration

A

generated by centripetal force

this acceleration keeps an object in its circular pathway (remember: the acceleration is always in the same direction as the net force)

64
Q

defn: dynamics

A

the study of forces and torques

65
Q

defn: translational motion

A

occurs when forces cause an object to move without any rotation

66
Q

what are the two things needed to solve any translational motion problem?

A
  1. free body diagrams
  2. Newton’s three laws
67
Q

when does translational equilibrium exist? what is this called?

A

exists only when the vector sum of all the forces acting on an object is zero

this is called the first condition of equilibrium

68
Q

why does an object experiencing translational equilibrium have constant velocity?

A
  1. when the resultant force upon an object is zero, the object will not accelerate (so the object is stationary OR is moving with a constant nonzero velocity)
  2. THUS an object experiencing translational equilibrium will have a constant velocity
69
Q

defn: rotational motion

A

occurs when forces are applied against an object in such a way as to cause the object to rotate around a fixed pivot point (the fulcrum)

70
Q

defn + aka: torque

A

application of force at some distance from the fulcrum

aka: moment of force

71
Q

defn: lever arm

A

the distance between the applied force and the fulcrum

72
Q

why is torque what generates rotational motion NOT the mere application of the force itself?

A

because torque depends not only on the magnitude of the force but also on the length of the lever arm and the angle at which the force is applied

73
Q

defn + aka: rotational equilibrium

A

exists only when the vector sum of all the torques acting on an object is zero

aka: second condition of equilibrium

74
Q

pair clockwise (cw) and counterclockwise (ccw) torques with positive and negative

A

CW = negative

CCW = positive

75
Q

what are the two possibilities of motion in the case of rotational equilibrium?

which is more common on the MCAT?

A
  1. not rotating at all (stationary) –> almost always the case on the MCAT
  2. rotating with a constant angular velocity

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