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UW - Physics 121 - Study Guide - Midterm

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Physics 121 Mechanics

Midterm #2 Study Guide

Lecture Section A, Professor: Kai-Mei C Fu

Note: This study guide will cover all material of the quarter leading up to the second midterm, as there was no study guide for material on the first midterm. Resources such as the textbook and My Labs and Mastering are good for practice problems, as well as resources provided by the professor.

This material is from chapters 1-6 (material prior to midterm 1) and chapters 7-10 (new material since midterm 1 but prior to midterm 2)

I. One Dimensional Motion

a. Representations

i. Essential first step to solving any problem

ii. Make visual representations (aka draw it)

iii. Physics is modeling the real world around us

If you want to learn more check out In this theory, what two inferences were darwin able to draw?

1. Make accurate and good representations and models

b. Position

i. Depends on an object’s location relative to an arbitrarily chosen reference point called the origin

c. Displacement

i. Does not depend on choice of reference axis or origin

ii. How much he/she/they moves

iii. Vector (has direction)

d. Distance traveled

i. Distance covered by a moving object along the path of its motion

ii. Will always be positive (unlike displacement)

e. Speed

i. The rate at which an x(t) curve rises with increasing time is called the slope of the curve

1. Less steep slope gives a slower speed

2. On position-time graphs

We also discuss several other topics like What are the 4 plant tissues?

f. Average Speed

i. The distance traveled divided by the time interval required to travel that distance

g. Average Velocity

i. The displacement of an object divided by the time

ii. Final and initial positions

iii. Ignore distance

II. One Dimensional Motion: Quantitative

a. Scalars and Vectors

i. Scalars: a number, positive or negative, and a unit of measure We also discuss several other topics like What percentage of the south american population would be considered urban?

1. Temperature, distance, time

ii. Vectors: a magnitude, always positive, a direction in space and a unit of measure

1. Displacement, velocity, position

b. Vector Notations

i. ∆��→ =����

→ −����

→

ii.����

→ = ����,����̂= ������̂

iii.����

→ = ����,����̂= ������̂

iv. ∆��→ = (���� − ����)��̂= ∆����̂

c. Adding and Subtracting Vectors Graphically

i. ----???? + ------???? = --------------???? If you want to learn more check out How does metabolism take place in the body?

d. Velocity as a Vector

i. X-component of the average velocity:

∆��=����−����

1. ����,������ =∆��

ii. Average velocity:

����−����

1.��→������= ����,��������̂=∆��→

∆�� We also discuss several other topics like What are the sub-divisions of long-term memory?

e. Motion at a Constant Velocity

i. ����,������ = ���� =∆�� If you want to learn more check out How was the republican coalition in the south easily broken?

∆��

1. Velocity: slope of apposition curve (derivative)

ii. ∆�� = ����∆��

1. Displacement: area under velocity curve (integral) iii. Instantaneous Velocity

∆��

∆��=����

����(derivatives)

III. Recap:

1. ���� = lim ∆��→0

a. Motion: x(t) = x0 + v0t = s(t)

b. In One Dimensional Motion

i. Position: measured with a coordinate system

1. Origin

2. Direction (along the x-axis)

3. Sense (positive and negative signs)

ii. All vector quantities (position, displacement, velocity) have a magnitude and direction (in a sense)

iii. Delta (∆) means “change in”

iv. Displacement is change in position: ∆���� = ���� − ����

c. Acceleration

i. Velocity and acceleration in the same direction = speeding up ii. Velocity and acceleration in opposite directions: slowing down iii. In position vs time: slope = velocity

iv. In velocity vs time: slope = acceleration

d. Motion with Constant Acceleration

i. Displacement is the area under the curve in the position versus time graph 1. ���� = ���� + ��0

ii. Acceleration is the area under the curve in a velocity versus time graph iii. Integrals ???? rectangles, triangles and trapezoids

1. ��̅=∆��

∆��

iv. Kinematic Equations: motion with a constant acceleration

v. Gravity = 9.81 m/s2

IV. Friction

a. In the absence of friction, objects moving a long a horizontal track keep moving without slowing down

V. Inertia

a. The tendency of an object to resist a change in its velocity

b. Determined entirely by the type of material of which the object is made and by the amount of that material contained in the object

VI. Systems

a. Extensive quantities are proportional to the size of the system.

b. Intensive quantities do not depend on the extent of the system

VII. Momentum

a.��→ = �� ∗��→

b. Change in momentum: ���� =−∆������

∆����������so ∆������ + ∆������ = 0

VIII. Momentum of a System

a. Can add up all momentums (p)

b. Isolated systems

i. A system with no external interactions is isolated

ii. No output or input of momentum

iii. If the p of the system changes, it cannot be an isolated system

iv. ∆��→ = 0 →��→��−��→��= 0 ] this is an isolated system

v. ∆��→ = ��̂] impulse system ???? general

IX. Types of Collisions

a. Elastic: The relative speeds before and after are the same

b. Inelastic: The relative speed after is lower than before

c. Totally Inelastic: The two objects move together after, so that the relative speed is reduced to zero

X. Kinetic Energy

a. In elastic collisions, the total KE is conserved

b. �� =12����2

XI. Internal Energy

a. Energy can be transformed from one object to another, or converted from one form to another, but it cannot be created or destroyed

b. Comparing

i. Elastic:

1. Relative speed unchanged

2. Reversible Process

ii. Inelastic:

1. Relative speed changed

2. Irreversible process (permanent)

c. Internal energy associated with the state of an object:

State ∆

Internal E

Temperature

Thermal E

Chemical

Chemical E

Reversible Shape

Elastic E

Phase

Transformation E

d. Closed Systems

i. No energy transfer across the boundary

ii. Change of physical state possible in isolated? Yes

iii. Change of physical state possible in closed? Yes

e. Elastic Collisions

i. Conservation of the system KE

ii. Newton’s cradle

XII. Inelastic Collisions

a. KE not conserved

b. Coefficient of restitution e

c. Conservation of Energy

i. E = K + Einternal

ii. For Closed Systems:

1. Ei = Ef

2. Ki + Eint,i = Kf + Eint,f

3. ∆�������� = −∆��

d. Explosive Separations

i. An explosion of an object is like a totally inelastic collision run backwards e. Inertial Reference Frames

i. An isolated object that is at rest remains at rest, and an object in motion keeps moving at a constant velocity

ii. Conservation of energy and momentum apply in inertial reference frames XIII. Principle Relativity

a. The laws of the universe are the same in all inertial reference frames moving at a constant velocity relative to each other (Newton’s Law of Inertia)

b. Zero-Momentum Reference Frame

i. Can always find a reference frame where the momentum of the system is zero

ii. Two important reference frames:

1. The one you are in (i.e. the Earth’s)

2. The zero-momentum reference frame (once in it, collision

calculations are simplified)

c. Galilean Relativity

i. Used to relate an event in two reference frames (A and B)

ii. Time of event in new reference frame

iii. Position

XIV. Center of Mass

a. For a continuous object, you replace the sum with integrals to find the center of mass

i. For symmetric objects, we rely on symmetry

b. Motion of Center of Mass: differentiation

c. A reference frame moving at the center of mass is the zero-momentum reference frame

d. Convertible (and translational) center of mass kinetic energy: K = Kcm + Kconv e. Changes in momentum and energy of a system are the same in any two reference frames moving at constant velocity relative to each other

XV. The effects of interactions

a. The interations are mutual influences between two objects that product ∆, either ∆������������ or ∆��ℎ������������

i. Two objects needed

ii. Momentum of isolated system of interacting objects is conserved before, during and after interaction

b. Potential Energy (PE????U)

i. The converted KE in a collision or interaction that is temporarily stored in reversible ∆�� of the arrangement of the system’s interacting components

ii. Mechanical energy (ME) = KE +PE (U)

c. Conversion of Energy

i. Closed system: total E constant

ii. Convert E between types

iii. Mechanical creates thermal

iv. Creation of thermal is dissipative and never fully recovered

d. Nondissipative Interactions

i. ∆��������ℎ = 0 ������ℎ ��������ℎ = �� + ��

e. Conservation of Momentum throughout the interaction gives us the relationship between accelerations

f. Energy conservation in a closed system: ∆�� = ∆�� + ∆�� + ∆���� (��ℎ������������) + ∆����ℎ (����������������) = 0

XVI. Momentum and Force

a. The vector sum of all forces exerted on an object equals the time rate of change in the momentum of the object

b. Identifying Forces

i. Contact: push, pull and rub

ii. Field: gravity, electric and magnetic

c. Translational Equilibrium and acceleration

i. An object at rest or moving at constant velocity is said to be in translational equilibrium

XVII. Motions for a single force

a. �������������� ��:∆��������������

∆��= ��������������,������

∆��������������

b. ����������: lim ∆��→0

∆��=����

����= ��������������

c. ������������������ℎ���� �������������� �� ������ ��: �� =����

����= ������

����= ����

i. Newton’s Second Law: F=ma

d. Generalizations

i. Single: F=ma

ii. Many: F1+F2+F3+…+Fn= ma

iii. Gravity: F= -mg

e. Hooke’s Law

i. Fby load on spring= k(x-x0)

ii. Fby spring on load= -Fby load on spring

iii. Fby spring on load= -k(x-x0) so -kx

f. Impulse (chapter 4)

i. J=∆p

XVIII. When a system is not isolated (i.e. p is not conserved), then the change in p is: ∆�� = �� = ��∆��

a. When a system is not closed (i.e. E is not conserved), then the change in E is: ∆�� = �� = ����∆��

b. External force and displacement must be in the same direction

c. Work can be positive, negative or zero

i. Positive if direction of F and the displacement are the same

ii. Negative if direction of F and the displacement are opposite

XIX. Remember: never pick a system in which friction lies at the boundary a. Mazur’s Energy Bar Diagrams

b. ∆�� = ���� − ���� =12��(����2 − ����2)

c. Variable force

i. Work is the area under steps of constant force (integral)

XX. Power

a. The rate at which energy is transferred or converted (�� =����

����)

b. The power delivered by a constant external force is:

i. �� = lim ∆��→0

∆��

∆��= lim ∆��→0

��

∆��= lim ∆��→0

��������∆��

∆��= ������������

c. If we change reference frames, motion that was in a straight line is no longer in a straight line

XXI. Normal Force

a. The normal and tangential component of the contact force behave differently so they are usually treated as two different forces, and are referred to respectively as the normal and friction forces

XXII. Static and Kinetic Friction Forces

a. Friction opposed the motion of two surfaces relative to each other

b. Friction exerted by surfaces that are not moving relative to each other is called static friction

c. Friction exerted by surfaces tat are moving relative to each other is called kinetic friction

XXIII. Work and Friction

a. The force of static friction is an elastic force

i. Similar to the normal force

ii. The deformations that take place undo themselves when the force that

caused them is removed

b. The force of kinetic friction is not an elastic force and so causes energy

dissipation

c. The force of static friction is an elastic force and so causes no energy dissipation d. Do not choose a system for which friction occurs at the boundary because you don’t know how much of the dissipated energy ends up on each side of the

boundary

e. The force of static friction CAN do work on a system

i. You CAN choose a system where STATIC FRICTION occurs at the

boundary

XXIV. Vector Algebra

a. Polar Coordinates

i. Radial coordinate r gives distance from the origin to the point (always

positive)

ii. Angular coordinate theta gives the angle between r and the x-axis, and is measured counterclockwise from the positive x-axis

b. Rectangular coordinates

XXV. Projectile Motion, Collisions and Momentum in 2D

a. See Mazur 10.7 and 10.8

XXVI. Work as the Product of 2 Vectors

a. See Mazur 10.9

XXVII. Coefficients of Friction

a. The maximum force of static friction exerted by a surface on an object is proportional to the force with which the object presses on the surface and does not depend on the contact area

b. ��s is the coefficient of static friction

c. ��k is the coefficient of kinetic friction

d. ��k < ��s always

***Sections 10.7, 10.8 and 10.9 are entirely equations and examples relevant to this exam***