Exam 1 - Physics

Physics

The most fundamental of sciences

• Study of matter and energy and their behavior through space and time

Almost everything we do in our daily life is based on..

Laws or principles of physics:

• Playing sports

• driving a car

• listening to music

What does Physics do?

Describes how the universe behaves:

• Describes the mechanisms and rules governing matter and energy through observation and mathematics

• Describes how specific mechanisms work, not the philosophical purpose behind them

Physics uses observations to create a framework to..

Describe how phenomena fit with the rest of the world

• Creating models that make predictions of how things behave

Framework

Conceptual / Mathematics

To ensure accuracy and reproducibility in Physics

Define the units in which the measurements are made

• Physics involves measurements of various quantities

Units are as important to measurements/calculations as the

Numbers they are associated with

• They set the scale and the physical nature of the quantity

Derived units

Units for other physical quantities

Prefixes do what?

They denote smaller or larger terms; they tell you how big or how small something is

Conversion of Units

Values can of course be measured in different units

• Very important to know how to convert between units

If units do not combine algebraically to the expected result

Conversion was not done correctly

• Only quantities with the same units can be added or subtracted

What are the standard SI units for

Mass: kg

Length: m

Time: s

Dimensional Analysis

A quantity with a unit requires a certain type of unit according to its physical nature

Dimension:

The physical nature and the type of unit

ISQ

International System of Quantities

• Length - [L]

• Mass - [M]

• Time - [T]

• Electric Current - [I]

• Temp. - [Θ]

• Amount of Substance - [N]

• Luminous Intensity - [J]

Dimensional Analysis: Speed

[L]/[T]

Dimensional Analysis: Acceleration

[L]/[T]²

Dimensional Analysis: Force

N = kgm/s² or [M][L]/[T]²

Is it possible for two quantities to have the same dimensions but different units?

Yes, there are many different units that can be used for one dimension

• Ex: units for the dimension of length can be meters, feet, inches, or km.

Is it possible for two quantities to have the same units but different dimensions?

No, if something has the same units, it will have the same dimensions, but if it has the same dimensions, it won’t always have the same units.

Can you always add two numbers that have the same dimensions?

No, if they have different units, you will have to convert the numbers to the same units to add/subtract

Trigonometry

A branch of mathematics studying relationships between sides and angles of triangles

Pythagorean Theorem

h² = ho² + ha²

Scalar

A quantity that can be described with a number and unit

• Ex: Temp, mass, time, density, and energy

Vector

A quantity that describes both magnitude and direction with units

• Ex: velocity, force, displacement, momentum, and acceleration

We use arrows to represent vectors

The direction of the arrow gives direction of the vector and the length of the arrow gives the magnitude of the vector

Scalars are written with italic symbols

V for volume

m for mass

t for time

Vectors are written with boldface symbols and with an arrow above them (sometimes only boldface)

𝐅⃗ for force
V for velocity
a for acceleration

Math done on vectors must take into account both…

Magnitude and direction of the vectors

• Easiest situation when vectors are colinear because the vectors point in the same direction

  • You can add them directly together when they point in same direction

  • R = A + B

What do you do if vectors are not colinear?

You use the Pythagorean Theorem and Trigonometry to solve

Multiplying a vector by a scalar changes the

Magnitude but not the direction

Multiplying a vector by -1 does what?

The direction is reversed while the magnitude remains the same

A vector with known direction and magnitude can be

Resolved into its components

Vector components give the most convenient method of adding/subtracting any number of vectors

Convert each vector into its components

• Each vector will have an x and y component

• Add/subtract all the corresponding colinear components

  • All x components add/subtract together and same with y-components

Components of final vector

Resultant components

• Can convert back to magnitude and direction

What are two aspects to any motion?

The movement itself and what caused it or changed it

Kinematics

Concepts that are needed to describe motion; no reference to forces

Dynamics

Effect of forces on motion

Mechanics

= Kinematics + dynamics

In order to describe motion of an object

Must be able to specify location of an object at all times

Displacement shows how far

The vector from an object’s initial position moved to its final position

• Magnitude: the shortest distance between the two positions

Final Displacement =

Initial position + displacement

Displacement and distance are

Not the same physical quantities

• The final position can be reached after many different paths; what matters is the final position with respect to the origin, not the path taken

Average Speed

The distance traveled divided by the time required to cover the distance

• ave. speed = distance / elapsed time: SI units are m/s

Speed is a

Scalar (number with a unit) and reveals nothing about direction of motion

Velocity

Helps describe the speed and direction of motion; is a vector

• Use displacement instead of distance

Average velocity

Ave V = Displacement / elapsed time

• V = (X - X0) / (t - t0)

Average Velocity is a

Vector that points in the same direction as displacement; it's positive in one direction, negative in the other.

Is the average speed of a vehicle a vector or a scalar quantity?

A scalar because it only includes magnitude. It is distance / time

Two buses depart from Chicago, one going to New York and one to San Francisco. Each bus travels at a speed of 30 m/s. Do they have equal velocities?

No, velocities include direction, so while they have the same speed because they have different direction the velocities will not be equal.

The average velocity for a trip has a positive value. Is it possible for the instantaneous velocity at a point during the trip to have a negative value?

Yes, average velocity depends on overall displacement and total time, the instantaneous velocity describes an object’s motion at one moment. So at one point in the trip the instantaneous velocity could be negative.

Acceleration

Describes how the velocity of an object changes during a given time interval

• Vector that points in the same direction as change in velocity

Average Acceleration

Ave. acceleration = Change in velocity / Elapsed time

• a = (V - V0) / (t - t0) or delta V / delta t

• Units are m/s²

Instantaneous Acceleration

An objects acceleration at a particular instant of time

What does constant acceleration mean?

The change in velocity is the same for each time interval

At one instant of time, a car and a truck are traveling side by side in adjacent lanes of a highway. The car has a greater velocity than the truck has. Does the car necessarily have the greater acceleration?

No, velocity just shows that the car is going faster in the same direction of the truck. It could be going at a constant speed while the truck is accelerating more but going slower.

An object moving with a constant acceleration slows down if the acceleration points in the direction opposite to the direction of the velocity. But can an object ever come to a permanent halt if its acceleration truly remains constant?

No, If acceleration is constant the object cannot remain permanently at rest

A runner runs half the remaining distance to the finish line every ten seconds. She runs in a straight line and does not ever reverse her direction. Does her acceleration have a constant magnitude?

No, her speed is decreasing since she runs half the remaining distance every 10s

The muzzle velocity of a gun is the velocity of the bullet when it leaves the barrel. The muzzle velocity of one rifle with a short barrel is greater than the muzzle velocity of another rifle that has a longer barrel. In which rifle is the acceleration of the bullet larger?

The shorter rifle will have the greater acceleration

A car is traveling along a straight road and is decelerating. Which one of the following statements correctly describes the car’s acceleration? (a) It must be positive. (b) It must be negative. (c) It could be positive or negative.

C. The acceleration vector of the car could point in the positive or the negative direction, so that the acceleration could be either positive or negative, depending on the direction in which the car is moving.

All objects at the same location above earth

Fall vertically with the same acceleration when ignoring gravity

If the distance is small compared to the earth’s radius

Acceleration remains essentially constant

Free-fall is the

Ideal motion of no air resistance and constant acceleration

• Acceleration due to gravity - g = 9.80m/s²

Equations of kinematics applied to free-fall motion: y for displacement since motion in vertical direction

v = 𝑣0 + 𝑎𝑡
𝑦 = 1/2(𝑣0 + 𝑣) 𝑡
𝑦 = 𝑣0𝑡 + 1/2 𝑎𝑡²
𝑣² = v0² + 2𝑎𝑦

Acceleration due to gravity

Always a downward-pointing vector

• Describes how speed increases for an object falling freely

Acceleration due to gravity also describes how

Speed decrease for an object moving upward under the influence of gravity alone

• The object eventually comes to a momentary halt and then falls back to earth

Free-fall

Object moving up or down under influence of gravity only

Noteworthy behaviors in free-fall

An object will always experience the same, constant downward acceleration due to gravity

• velocity changes but not acceleration

• acceleration is the rate at which velocity changes

An object traveling upwards:

Gravity causes its speed to decrease to zero

• In downward motion: gravity causes an object to regain the lost speed

Time for the object to go up is

Equal to the time for it to come down

• Total travel time is twice the time for upward motion

For an object traveling upward and returning to its release point or starting point

Displacement for the entire trip is y = 0m

At any displacement y above the release point

An objects speed in the upward trip equals the speed at the same point during the downward trip

Suppose you are driving due east, traveling a distance of 1500 m in 2 minutes. You then turn due north and travel the same distance in the same time. What can be said about the average speeds and the average velocities for the two segments of the trip? (a) The average speeds are the same, and the average velocities are the same. (b) The average speeds are the same, but the average velocities are different. (c) The average speeds are different, but the average velocities are the same.

B. Velocity includes direction and since the the two points go in different directions the velocities are different.

Projectile Motion

Motion of object thrown or projected into air, subject to only acceleration of gravity with no air resistance

AT max hieght of trajectory or apex

Vertical component of velocity is zero while the horizontal component of velocity is not zero

Range R:

Horizontal distance traveled by the projectile

Hang time

Time of projectile in air

• Determined by acceleration due to gravity