Chapter 1: Kinematics and Dynamics Flashcards
1
Q
Biology is chemistry. Chemistry is physics. Physics is life.
A
That’s it. That’s the card.
2
Q
What are SI units? What are the SI units (7 base units and 8 derived units).
A person helping could ask me different units or quantities or symbols rather than have me rattle them all off.
A
The International System of Units (SI) is the modern metric system and the world’s most widely used measurement system, especially in scientific fields. It’s a standardized system based on the number 10, with seven base units and derived units.
3
Q
What are the SI prefixes for size factors?
A
4
Q
What is an angstrom? A nanometer? An electron-volt? Where would you use these units?
A
We would use these units for the molecular, atomic, or subatomic level.
5
Q
Concept check 1.1 kinematics and dynamics page 9 question 1
A
6
Q
Concept check 1.1 kinematics and dynamics page 9 question 2
A
7
Q
Do you need to memorize the SI system?
A
Yes, you need to memorize the SI system. Start with these two table tables.
8
Q
What is a vector? Was it a scalar? Give three examples of both.
A
Vectors or numbers that have magnitude and direction. Quantities include displacement, velocity, acceleration, and force.
Scaler or numbers that have magnitude only and no direction. Scaler quantities include distance, speed, energy, pressure, and mass.
9
Q
How are vectors and scalar quantities indicated in text?
A
Vectors may be represented by arrows, the direction of the arrow indicates the direction of the vector. The length of the arrow is usually proportional to the magnitude of the vector quantity. Common notations for a vector quantity are either an arrow or bold face.
Scalar quantities are generally represented with italic type.
10
Q
What is the sum or difference of two or more vectors called? How do you add vectors using the tip to tail method?
A
The summer difference of two or more vectors is called the resultant of the vectors.
If you take the difference (and need to subtract a vector) take the opposite direction and same magnitude, tip to tail.
11
Q
How do you find the resultant of a vector by breaking it down into its components?
A
Use horizontal and vertical components (x and y components respectively) or parallel or perpendicular to some other surface.
12
Q
Example component vector calculation page 12
A
13
Q
What is sin, cos, and tan of 0°, 30°, 45°, 60°, and 90°
A
14
Q
How to calculate magnitude of vector (V) given A and B.
A
15
Q
Example magnitude vector calculation page 12
A
16
Q
How do you find resultant vector (R) of V1+V2+V3.
There are four steps. What are they?
A
The X component of a result in vector is simply the sum of the X components of the vectors being added. Similarly, the Y component of a resultant vector is simply the sum of the Y components of the vectors being added.
17
Q
How can the angle of a resultant vector be calculated?
A
Given X and Y.
Note: the inverse tangent calculation is beyond the scope of the MCAT.
18
Q
How do you subtract a vector?
A
When you subtract vectors, you are simply flipping the direction of the vector being subtracted, and then following the same rules as normal: adding tip to tail.
19
Q
How do you multiply vectors by scalars?
A
When a vector is multiplied by a scalar, its magnitude will change. It will be either parallel or anti-parallel to its original direction.
20
Q
What is the product of two vector values? What are the two types of methods? How do you multiply vectors by other vectors? Whats the rule for direction of vector using one of the products?
A
Dot products produce a scalar magnitude value of the two vectors.
Cross products produce a vector value that produces a perpendicular direction solved by using the right hand method.
21
Q
In vector calculus, what is a dot product?
A
To generate a scalar product like work, multiply the magnitudes of the two vectors of interest (force and displacement) and the cosine of the angle between the two vectors.
22
Q
When generating a third vector, like torque, we need to determine magnitude AND direction. How would we do this?
A
Multiply the magnitudes of the two vectors of interest (for torque it would force and lever arm) and the sine of the angle between the two vectors. Use the right hand rule to determine the direction. In vector calculus, this is called the cross product. Which is:
Important: the first vector always being pointed to by the thumb and the second vector by the middle finger (fingies).
23
Q
Example page 15 magnitude and direction of resultant vectors cross product (obv because there is a resultant vector)
A
Couple things.
Recognize that the cross product will make a vector quantity, in the case Newton for vector A, meter for vector B. The resultant vector of the cross product is Nm, a unit of torque.
Right hand rule. Thumb toward first vector in the calculation, fingers toward second.
If confused, draw the vectors.
Notice the notation for into and out of the page.
24
Q
Does the order of cross product and dot product matter?
A
25
Concept check 1.2 vectors and scalars page 16 question 1-4
26
What is a commutative function? How does this relate to vector calculations?
A "commutative function" refers to a function where the order of its inputs does not affect the output, meaning if you swap the order of the arguments when applying the function, the result remains the same; essentially, it exhibits the "commutative property" often seen in basic arithmetic operations like addition and multiplication where "a + b" equals "b + a" and "a * b" equals "b * a" respectively.
In vector sum, difference, and product:
Vector sums are commutative in that the order doesn’t matter.
Vector difference is not commutative in that A-B and B-A will have same magnitude but opposite directions.
Vector product is not commutative meaning that switching the order of the vectors in the cross product results in a negative sign change, while the magnitude itself remains the same. Direction is order specific (recall right hand rule).
27
What are the three basic quantities that relate to kinematics? Briefly define them.
Displacement (x or d): change in position of space, a vector quantity measured in meters and direction.
Velocity (v): rate of change of displacement, is a vector quantity measured in meters per second.
Acceleration (a): rate of change of velocity, is a vector quantity and measure in meters per second squared.
28
What is displacement? What is the difference between displacement and distance traveled?
29
Example page 17 displacement and distance traveled
30
What is velocity? Units? Does the velocity vector equal the displacement vector? Are speed and velocity the same?
Velocity is a vector quantity, speed is a scalar quantity.
31
Compare and contrast instantaneous speed and instantaneous velocity, average speed and average velocity.
Instantaneous speed of an object will always be equal to the magnitude of the objects instantaneous velocity, which is a measure of the average velocity as the change in time (deltat) approaches zero. As a measure of speed, instantaneous speed is a scalar number.
Average speed will not necessarily always be equal to the magnitude of the average velocity. This is because average velocity is the ratio of the displacement vector over the change in time (and is a vector), whereas average speed (which is scalar) is the ratio of the total distance traveled over the change in time.
Average speed accounts for actual distance traveled, whereas average velocity does not.
32
Use earths orbit to exemplify average speed and average velocity.
33
Concept check page 18 questions 1,2,3.
34
How many seconds are in an hour? A day? A month? A year?
35
What is force? Units?
36
What is gravity? Units? How do you calculate gravitational force between two objects? What is the gravitational force near the earths surface?
Gravity is an attractive force that is felt by all forms of matter. All object exert gravitational forces on each other.
37
What would happen to the force of gravity between two objects if the mass of one was tripled? If the distance between them was halved? Distance between them doubled?
38
Example page 20 gravitational force calculation
The trick with this equation was in the algebra.
Recognizing that 6.66 is 20/3 and 1.66 is 5/3.
Also being comfortable that multiplying exponents is addition of exponents, and dividing by a negative exponent is adding the exponents together (minus a negative).
39
What is friction? In which direction does friction force always oppose? Where are the two kinds of friction?
Friction is a type of force that opposes the movement of objects. Friction forces always oppose an objects motion and cause it to slow down or become stationary. The two types of friction are static and kinetic.
40
What is static friction (f sub s)? What is the inequality that describes the magnitude of static friction? What is the coefficient of static friction? What is the normal force?
Static friction exist between a stationary object and the surface upon which it rests. The inequality that describes the magnitude of static friction is shown in the image.
The coefficient of static friction is a unit-less quantity that is dependent on the two materials in contact (experimentally determined).
The normal force is 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.
There’s a range of possible values for static friction. The minimum is zero, the maximum value of static friction can be calculated from the right side of the inequality equation. Do not assume that objects that are stationary are experiencing a maximal static force of friction.
41
What is kinetic friction (f sub k)? Does a wheel experience kinetic friction? What are two important distinctions between the equation for kinetic friction in the inequality equation for static friction?
Kinetic friction exist between a sliding object and the surface over which the object slides. A wheel does not experience kinetic friction, but maintains an instantaneous point of static contact with the road, and therefore experiences static friction.
The two important distinctions between the equation for kinetic friction in the equation for static friction are:
First. Kinetic friction equation has an equals sign. This means that kinetic friction will have a constant value for any given combination of a coefficient of friction in a normal force. It does not matter how much surface area is in contact or even the velocity of the sliding object.
Second. The two equations have a different coefficient of friction. Coefficient of static friction is always larger than the coefficient of kinetic friction.
42
What is mass? What is weight? What are the units for mass and weight? Are they vectors or scalar? What is the equation that relates mass and weight?
Mass (m) is a measure of the body inertia, the amount of matter in the object. Mass is a scalar quantity and has magnitude only. The SI unit for mass is the kilogram.
Weight (Fg) is a measure of gravitational force on an object’s mass. Weight is a force, it is a vector quantity with units in newtons (N = kg m/s^2).
43
Where is the center of mass of a uniform object?
The center of mass of the uniform object is at the geometric center of the object.
44
What is acceleration (a)? Is acceleration a vector quantity? What are the units of acceleration? What is deceleration? What is the equation for average acceleration? What is the equation for instantaneous acceleration? How can you determine acceleration on a graph of velocity versus time?
Acceleration (a) is the rate of change of velocity that an object experiences as a result of some applied force. Acceleration is a vector quantity and is measured in SI units of meters per second squared. Acceleration in the direction opposite the initial velocity may be called deacceleration.
On a graph of velocity versus time, the tangent to the graph at any time t, which corresponds to the slope of the graph at that time, indicates the instantaneous acceleration. If the slope is positive, then the acceleration is positive and in the same direction as the velocity. If the slope is negative, then the acceleration is negative and in the opposite direction of velocity (deceleration).
45
Concept check 1.4 page 24 questions 1-4 forces and acceleration
46
What are Newtons three laws of motion?
47
Objects can undergo only two types of motion (this is true, but what this statement is getting at is regarding acceleration)?
Objects can undergo only two types of motion:
Constant motion (with no acceleration)
Changing motion (with acceleration)
48
What is linear motion? What is the most common presentation of linear motion problems on the MCAT?
In linear motion, the objects, velocity and acceleration are along the line of motion, so the pathway of the moving object continues a long, a straight line. Linear motion can refer to vertical or horizontal paths; inclined surface of a ramp will provide a path for linear motion at some angle. Following objects exhibit linear motion with constant acceleration (acceleration due to force of gravity).
On the MCAT, the most common presentations of linear motion problems involve objects, such as balls, being dropped to the ground from some starting height.
49
One dimensional motion can be fully described by four equations. What are those equations and their variables?
What is the acceleration due to gravity? When, by convention, will x displacement be substituted for y?
50
Kinematic example page 27 part A
51
Kinematic example page 27 part B
52
Ball dropped from 40m. What is final velocity and how long does it take to hit the ground?
Need kinematics to solve. We can look at the known variables and fit it with an equation. In this case, we knew initial velocity (0) and acceleration (-10 m/s^2) and displacement (-40 m). Can solve for time and velocity.
We can use potential energy and kinetic energy to solve for velocity in this problem as well. Try it out.
We need to select the cinematic equation that accounts for displacement to solve for time. Initial velocity is zero, y is 40.
53
Ball dropped from 5 m. What is final velocity and how long does it take to hit the ground? What is the average velocity?
Need kinematics to solve. We can look at the known variables and fit it with an equation. In this case, we knew initial velocity (0) and acceleration (-10 m/s^2) and displacement (-5 m). Can solve for time and velocity.
I made this card to demonstrate that these calculations may not be instantly intuitive.
54
Ball dropped from 5 m. Use conservation of energy to solve for velocity.
55
Relate resistance, drag force, and terminal velocity.
56
What are three important considerations to make when using kinematic equations?
Constant acceleration: Kinematic equations only work when the acceleration of an object is constant.
One-dimensional motion: These equations are typically used for motion in a straight line (one dimension).
Units: Ensure all values are in consistent units before calculations.
57
What is projectile motion?
58
The amount of time that an object takes to get to its maximum height is the same time it takes for the object to fall back down to the starting height. How is this useful?
59
Projectile motion example page 28 part A
60
Projectile motion example page 28 part B
61
A ball is dropped from 10 m. How long does it take to hit the ground?
62
What are inclined planes? How do we calculate force of gravity for inclined planes?
Inclined planes are another example of motion and two dimensions. When working with an inclined plane question, it is often best to divide force vectors into components that are parallel and perpendicular to the plane. Most often, gravity must be split into components for these calculations.
63
Example page 30 inclined planes.
The block in this example has two forces acting on it:
the normal force, which is perpendicular to the surface.
And gravity, which point straight down.
Draw a picture of the incline plane and the object.
Because gravity is not in the same coordinate system as the normal force, one of the two forces must be split into components. In this case, because we are concerned with magnitude of the normal force (which is perpendicular to the plane) and the acceleration (which is parallel to the plane), we should split the force of gravity into parallel and perpendicular components.
We can take those perpendicular components and sell for normal force and acceleration of the block.
64
What is circular motion? What is the displacement of an object undergoing circular motion upon completion of one cycle? What is uniform circular motion? What is the centripetal force? What is centripetal acceleration? What is the equation that describes circular motion?
Circular motion occurs when forces cause an object to move in a circular pathway. Upon completion of one cycle, the displacement of the object undergoing circular motion is zero.
In uniform, circular motion, the instantaneous velocity vector is always tangent to the circular path. This means that the object moving in a circular path has a tendency to break out of its circular pathway and move in a linear direction along the tangent.
The centripetal force is what keeps the object from moving in a linear direction, which always points radially inward. We can resolve the forces into radial and tangential components in uniform circular motion, the tangential force is zero because there is no change in the speed of the object.
As a force, this centripetal force generates centripetal acceleration. Force and acceleration are vectors, and the acceleration is always in the same direction as the net force. That it is the acceleration generated by the centripetal force that keeps an object in it circular pathway.
Centripetal force can be caused by tension, gravity, electrostatic forces, or other forces.
65
Concept check page 1.6 motion with constant acceleration question 1
66
Concept check page 1.6 motion with constant acceleration question 2
For horizontal displacement, we need to maximize the product of sign in cosine. This occurs at sin45° in cos45°.
For vertical displacement, this is somewhat of a trick question. The vertical displacement will be zero regardless of the angle of launch because the object returns to the same level it was launched from. In order to maximize distance traveled, the object needs to be launched straight in the air (sin90°=1 with zero horizontal component)
67
What is the equation for centripetal acceleration?
68
What is the study of forces and torques called?
The study of forces and torques is called dynamics. This requires us to be familiar with analyzing forces, especially with free body diagrams, as well as with the special conditions for translational and rotational equilibrium.
69
What is a free body diagram?
A free body diagram is a diagram that represents forces and the effects diagrammatically. When dealing with dynamics, always draw a quick picture of what is happening in the problem; this will keep everything and its proper relative position and help prevent simple mistakes.
70
Example page 33 free body diagrams
71
Draw a free body diagram for a snake on an inclined plane like KC showed us.
72
No acceleration, and therefore no net force on the object, does this mean velocity equals zero?
If there is no acceleration, then there is no net force on the object. This means that any object with a constant velocity has no net force acting on it. However, just because the net force equals zero does not mean the velocity equals zero, it means the velocity is constant.
73
What is translational equilibrium (also known as the first condition of equilibrium)?
Translational equilibrium exists only when the vector sum of all of the force is acting on object is zero. This is called the first condition of equilibrium, and it is merely a reiteration of newtons first law stating that when the resulting force upon an object is zero, the object will not accelerate. This could mean that the object is stationary, but it could just as well mean that the object is moving with a constant non-zero velocity.
THUS, AN OBJECT EXPERIENCING TRANSLATIONAL EQUILIBRIUM WILL HAVE A CONSTANT VELOCITY: BOTH A CONSTANT SPEED (WHICH COULD BE ZERO OR A NON-0 VALUE) AND A CONSTANT DIRECTION.
74
Example page 35 translational equilibrium
Identify in the question that this is static equilibrium telling you that all velocities are constant, but furthermore that velocity is zero.
First thing to do is write a free body diagram of A and a free body diagram of B.
Recognize that the sum of the forces must equal zero, and therefore, each other, in order for this system to be in static equilibrium. In this case, it was some force A equals force of tension connecting to some force B. The free body diagrams in opposition to each other would be force of static friction A equals force of gravity B.
We found that we could cancel g in this calculation.
75
What is rotational motion?
Rotational motion occurs when forces are applied against an object in such a way as to cause the object to rotate around a fixed pivot point known as the fulcrum. Application of force at some distance from the fulcrum generates torque, or the moment of force. The distance between the applied force and the fulcrum is termed the lever arm.
It is the torque that generates rotational motion, not the mere application of the force itself. This is because torque depends not only on the magnitude of the force, but also the length of the lever arm and the angle at which the force is applied.
76
What is the equation for rotational motion? Is it a cross product or a dot product?
77
Use the right hand rule to determine the toque vector for the following:
78
What is rotational equilibrium (the second condition of equilibrium)? When does it exist? Are torques that generate clockwise rotation considered positive or negative? Are torque that generate counterclockwise rotation positive or negative?
Rotational equilibrium exists only when the vector some of all the torques acting on an object is zero, this is called the second condition of equilibrium. In rotational equilibrium, it must be that all of the positive torques exactly council out all the negative torques. Similar to the behavior defined by translational equilibrium, there are two possibilities of motion in the case of rotational equilibrium.
79
Example page 37 rotational equilibrium
80
Can a moving object be an equilibrium? Why or why not?
A moving object can be in either translational or rotational equilibrium, or both. Translational equilibrium when we requires the net force on an object to be zero, its velocity is constant. The corresponding condition in rotational equilibrium is that net torque equals zero, its angular velocity is constant.
Said a different way: A moving object can be in equilibrium if it is moving with a constant velocity, meaning it has no acceleration; in this state, all the forces acting on it are balanced, resulting in a net force of zero, which is the key characteristic of equilibrium.
Said a different different way: a system in equilibrium is defined as the net force is equal to zero. This means that the velocity is constant, but does not necessarily mean that the object is not moving.
81
If there is an object three times as heavy as you can lift, how would a lever be used to lift the object where would the fulcrum need to be placed?
If the object is three times heavier than you can lift, then the lever arm would be need to be three times longer on your side than it is on the objects side so that you may apply a torque that is three times the force that you can apply.
82
Kinematic and dynamic mastery page four question 1
83
Kinematic and dynamic mastery page four question 2
I initially made a mistake and equated the force as acceleration. Force is not acceleration. Force is mass times acceleration.
I solved this equation two separate ways, which is kind of cool.
I used kinematics and ultimately got to the answer (in purple)
However, an easier and more straightforward way would be to recognize that acceleration is change in velocity over change in time (in black)
84
Kinematic and dynamic mastery page four question 3
Recognize that the answers are in kilometers per hour, and we are given a time in seconds. We will have to do a conversion from seconds to hours, kilometers is fine.
I immediately went to kinematics to solve this problem, which is fine. However, we need to once again realized is acceleration is change in velocity over change in time.
Pay attention to the sign of the answer. We plugged in negative acceleration and also negative velocity to get a positive acceleration value. However, in the book they signed positive average acceleration and a negative velocity getting a negative acceleration and made it positive because it asked for the magnitude of the acceleration, which is a positive number.
85
Kinematic and dynamic mastery page four question 4
86
Kinematic and dynamic mastery page four question 5
87
Kinematic and dynamic mastery page four question 6
88
Kinematic and dynamic mastery page four question 7
I set up this problem great, but ran into a few issues.
I intuitively knew that the X component of the force of gravity was the acceleration force on the plane, but did not represent that balancing force in my free body diagram. Remember to represent all forces on your free body diagram, in this instance, including the force of static friction (which is the opposing force of the acceleration vector in the X direction)
My second error was mistaking the acceleration vector on the X axis to be mgcostheta. THE ACCELERATION VECTOR ON THE X AXIS OF AN INCLINE PLANE IS mgsintheta.
Plug and play.
89
Kinematic and dynamic mastery page four question 8
90
Kinematic and dynamic mastery page four question 9
91
Kinematic and dynamic mastery page four question 10
92
Kinematic and dynamic mastery page four question 11
We could make intuitive sense of this question, but we always need to be careful in trusting or intuition too much. We know that the system is static equilibrium, and if the parent weighs more than the child the parent will need to be closer to the full room than the child is. This eliminates C and D. A doesn’t make sense (refer to picture if it doesn’t make sense). This leaves option B as the answer.
Image shows calculation
93
Kinematic and dynamic mastery page four question 12
Couple things about this question.
The only information you need to know to solve this is the initial velocity (r), launch angle (30°), and acceleration due to gravity (-10 m/s^2). The distance the ball traveled in the horizontal direction is immaterial.
Calculate the Y component of the initial velocity using rsintheta (12sin(30°)). This will be your initial velocity (the ball just launched). Your final velocity will be zero (the ball reached its maximum height at velocity 0). Acceleration is due to gravity.
Super interesting. If you calculate the Y component of the velocity vector and plug it in for final velocity, you will get a negative height. This makes sense because if the final velocity was 6 m/s, and the initial velocity was zero (ball at top of arc, and ball at ground, respectively) this calculates it the other way around, meaning the ball fell 1.8 m, therefore the negative sign.
94
Kinematic and dynamic mastery page four question 13
95
Kinematic and dynamic mastery page four question 14
96
Kinematic and dynamic mastery page four question 15
97
Equations from chapter 1
98
KC math and physics.
Bottom left: derived kinematic equations.
Top left: applied example of calculus using S=Q/T
Bottom rightish: cross product complexity of multiple dimensions
99
KC derived kinematics
