Exam #1 Review - Physics Laboratory

Flashcards covering key concepts, formulas, calculations, and visual graphs from Experiments #1-#4 in Physics Review for Exam #1.

What does the slope ($m$) of a function $y(x)$ describe in physics, and how is it calculated?

It describes the way a function changes, calculated as $m = \frac{\text{Δ}y}{\text{Δ}x} = \frac{y_2 - y_1}{x_2 - x_1}$.

How is the unit for the slope of a line determined from a graph?

$$\text{Unit for slope} = \frac{\text{Unit of } y\text{-axis}}{\text{Unit of } x\text{-axis}}$$

How is the unit for the y-intercept determined from a graph?

$$\text{Unit for y-intercept} = \text{Unit of } y\text{-axis}$$

In a graph of Work ($W = m \cdot a \cdot d$) on the y-axis in $\text{N}\cdot\text{m}$ versus Distance ($d$) on the x-axis in $\text{m}$, what does the slope represent?

The slope represents net force ($F = m \cdot a$), with units of $\frac{\text{N}\cdot\text{m}}{\text{m}} = \text{N}$.

Given a Work versus Distance graph with line equation $y = 0.8x$ and an acceleration of $4\,\text{m/s}^2$, what is the mass of the object?

$$m = \frac{\text{Slope}}{a} = \frac{0.8\,\text{N}}{4\,\text{m/s}^2} = 0.2\,\text{kg}$$

In a linear graph of Velocity ($v$) versus Time ($t$) following $v = a t + v_o$, what do the slope and y-intercept represent?

The slope represents acceleration ($a$), and the y-intercept represents initial velocity ($v_o$).

If the equation of a line for a velocity versus time graph is $y = 2x + 5$, what are the acceleration and initial velocity of the object?

Acceleration $a = 2\,\text{m/s}^2$ and initial velocity $v_o = 5\,\text{m/s}$.

What four sums must be calculated first when finding a best fit line manually using Least Square Regression?

$\sum X$, $\sum Y$, $\sum (XY)$, and $\sum X^2$

What is the formula for calculating the slope ($m$) in Least Square Regression?

$$m = \frac{N \sum (XY) - \sum X \cdot \sum Y}{N \sum X^2 - (\sum X)^2}$$

What is the formula for calculating the y-intercept ($b$) in Least Square Regression?

$$b = \frac{\sum Y - m \sum X}{N}$$

What are the standard units given for distance, time, mass, speed/velocity, and acceleration?

Distance $\rightarrow \text{meter}$, Time $\rightarrow \text{second}$, Mass $\rightarrow \text{kilogram}$, Speed/velocity $\rightarrow \text{m/s}$, Acceleration $\rightarrow \text{m/s}^2$

How do you convert a printer width of $18\,\text{in.}$ to meters given $1\,\text{in.} = 2.54\,\text{cm}$ and $100\,\text{cm} = 1\,\text{m}$?

$$18\,\text{in.} \times \frac{2.54\,\text{cm}}{1\,\text{in.}} \times \frac{1\,\text{m}}{100\,\text{cm}} = 0.46\,\text{m}$$

What does the density ($\rho$) of a substance describe, and what is its mathematical formula?

Density describes the compactness of its matter or mass, given by $\rho = \frac{m}{V} = \frac{\text{mass}}{(\text{length})^3}$.

What are two typical units used for density?

$\text{g/cm}^3$ and $\text{kg/m}^3$

Does this sphere model represent a substance that is 'More Dense' or 'Less Dense'?

It represents a 'More Dense' substance because the particles are tightly packed together within the volume.

What is the definition and formula for average velocity ($v_{\text{average}}$)?

Average velocity is the total change in position divided by the total change in time: $v_{\text{average}} = \frac{\text{Δ}x}{\text{Δ}t} = \frac{x_2 - x_1}{t_2 - t_1}$.

What feature of a Position versus Time graph represents the average velocity?

The slope of the Position versus Time graph represents average velocity ($\text{Slope} = \frac{\text{Δ}x}{\text{Δ}t} = v_{\text{Ave}}$).

Based on this Position versus Time graph, what is the calculated average velocity between Start ($t = 3\,\text{s}, x = 15\,\text{m}$) and End ($t = 14\,\text{s}, x = 70\,\text{m}$)?

$$v_{\text{avg}} = \frac{70\,\text{m} - 15\,\text{m}}{14\,\text{s} - 3\,\text{s}} = \frac{55\,\text{m}}{11\,\text{s}} = 5.0\,\text{m/s}$$

What feature of a Velocity versus Time graph represents average acceleration?

The slope of the Velocity versus Time graph represents average acceleration ($\text{Slope} = \frac{\text{Δ}v}{\text{Δ}t} = a_{\text{Ave}}$).

Based on this Speed of Object Versus Time graph, what is the average acceleration between $0.25\,\text{s}$ and $1\,\text{s}$?

$$\text{Slope} = \frac{100\,\text{m/s} - 40\,\text{m/s}}{1\,\text{s} - 0.25\,\text{s}} = \frac{60\,\text{m/s}}{0.75\,\text{s}} = 80\,\text{m/s}^2$$

How is height ($h$) expressed for a freely falling body dropped from rest ($v_o = 0$) at height $y_o = h$ to ground ($y = 0$)?

Starting with $y = y_o - v_o t - \frac{1}{2}g t^2$, substituting $y = 0$, $y_o = h$, and $v_o = 0$ gives $0 = h - \frac{1}{2}g t^2$, which simplifies to $h = \frac{1}{2}g t^2$.

What is the value of acceleration due to gravity ($g$) for all freely falling objects in a vacuum near Earth's surface?

$$g = 9.8\,\text{m/s}^2$$

In free fall motion, what does a net force lead to?

Acceleration