Energy Mass Patterns - Middle School Physical Science
Card 1 of 25
Which option best describes $KE$ vs. $m$ at constant $v$: proportional, inverse, or exponential?
Which option best describes $KE$ vs. $m$ at constant $v$: proportional, inverse, or exponential?
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Proportional. Direct proportionality shown by straight line through origin.
Proportional. Direct proportionality shown by straight line through origin.
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Identify the dependent variable on a graph designed to show how $KE$ changes with mass at constant $v$.
Identify the dependent variable on a graph designed to show how $KE$ changes with mass at constant $v$.
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Kinetic energy $KE$ (y-axis). We measure how kinetic energy responds to changes in mass.
Kinetic energy $KE$ (y-axis). We measure how kinetic energy responds to changes in mass.
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Identify the independent variable on a graph designed to show how $KE$ changes with mass at constant $v$.
Identify the independent variable on a graph designed to show how $KE$ changes with mass at constant $v$.
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Mass $m$ (x-axis). We control mass to observe its effect on kinetic energy.
Mass $m$ (x-axis). We control mass to observe its effect on kinetic energy.
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Using slope $= \frac{1}{2}v^2$, find $v$ if the $KE$ vs. $m$ slope is $8$.
Using slope $= \frac{1}{2}v^2$, find $v$ if the $KE$ vs. $m$ slope is $8$.
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$v = 4$. If $\frac{1}{2}v^2 = 8$, then $v^2 = 16$, so $v = 4$.
$v = 4$. If $\frac{1}{2}v^2 = 8$, then $v^2 = 16$, so $v = 4$.
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Choose the correct comparison at constant $v$: if $m_1 = 3m_2$, what is $\frac{KE_1}{KE_2}$?
Choose the correct comparison at constant $v$: if $m_1 = 3m_2$, what is $\frac{KE_1}{KE_2}$?
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$\frac{KE_1}{KE_2} = 3$. Direct proportionality: if mass triples, kinetic energy triples.
$\frac{KE_1}{KE_2} = 3$. Direct proportionality: if mass triples, kinetic energy triples.
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Find the slope from two points on a $KE$ vs. $m$ graph: $(2,6)$ and $(5,15)$.
Find the slope from two points on a $KE$ vs. $m$ graph: $(2,6)$ and $(5,15)$.
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Slope $= 3$. Slope $= \frac{\Delta KE}{\Delta m} = \frac{15-6}{5-2} = \frac{9}{3} = 3$.
Slope $= 3$. Slope $= \frac{\Delta KE}{\Delta m} = \frac{15-6}{5-2} = \frac{9}{3} = 3$.
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A $KE$ vs. $m$ graph is a straight line not through the origin. Identify the most likely issue.
A $KE$ vs. $m$ graph is a straight line not through the origin. Identify the most likely issue.
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Nonzero offset or measurement/graphing error. Line should pass through origin; offset suggests error or non-zero intercept.
Nonzero offset or measurement/graphing error. Line should pass through origin; offset suggests error or non-zero intercept.
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Identify the correct equation form for a $KE$ vs. $m$ line at constant speed: $KE = km$ or $KE = km^2$.
Identify the correct equation form for a $KE$ vs. $m$ line at constant speed: $KE = km$ or $KE = km^2$.
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$KE = km$. Linear relationship has form $y = kx$ where $k = \frac{1}{2}v^2$.
$KE = km$. Linear relationship has form $y = kx$ where $k = \frac{1}{2}v^2$.
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If mass is cut in half while speed stays constant, what happens to kinetic energy?
If mass is cut in half while speed stays constant, what happens to kinetic energy?
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$KE$ is cut in half. Direct proportionality means if $m$ halves, $KE$ halves too.
$KE$ is cut in half. Direct proportionality means if $m$ halves, $KE$ halves too.
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If mass doubles while speed stays constant, what happens to kinetic energy?
If mass doubles while speed stays constant, what happens to kinetic energy?
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$KE$ doubles. Direct proportionality means if $m$ doubles, $KE$ doubles too.
$KE$ doubles. Direct proportionality means if $m$ doubles, $KE$ doubles too.
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What does the slope represent on a graph of $KE$ (y) versus $m$ (x) at constant $v$?
What does the slope represent on a graph of $KE$ (y) versus $m$ (x) at constant $v$?
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Slope $= \frac{1}{2}v^2$. From $KE = \frac{1}{2}v^2 \cdot m$, the coefficient of $m$ is the slope.
Slope $= \frac{1}{2}v^2$. From $KE = \frac{1}{2}v^2 \cdot m$, the coefficient of $m$ is the slope.
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Which graph shape shows $KE$ vs. $m$ when speed is constant: straight line or curve?
Which graph shape shows $KE$ vs. $m$ when speed is constant: straight line or curve?
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Straight line through the origin. Direct proportionality between $KE$ and $m$ creates a linear relationship through $(0,0)$.
Straight line through the origin. Direct proportionality between $KE$ and $m$ creates a linear relationship through $(0,0)$.
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State the kinetic energy formula that relates kinetic energy to mass and speed.
State the kinetic energy formula that relates kinetic energy to mass and speed.
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$KE = \frac{1}{2}mv^2$. Shows how kinetic energy depends on both mass and velocity squared.
$KE = \frac{1}{2}mv^2$. Shows how kinetic energy depends on both mass and velocity squared.
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Identify the correct unit pattern on a $KE$ vs. $m$ graph: $KE$ in joules and $m$ in what unit?
Identify the correct unit pattern on a $KE$ vs. $m$ graph: $KE$ in joules and $m$ in what unit?
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Kilograms (kg). Standard SI unit for mass in physics calculations.
Kilograms (kg). Standard SI unit for mass in physics calculations.
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A $KE$ vs. $m$ line becomes steeper in a second trial. Identify what changed if only $v$ can change.
A $KE$ vs. $m$ line becomes steeper in a second trial. Identify what changed if only $v$ can change.
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Speed increased. Steeper slope means larger $\frac{1}{2}v^2$, indicating higher speed.
Speed increased. Steeper slope means larger $\frac{1}{2}v^2$, indicating higher speed.
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Identify which trial has higher speed: Trial A slope $= 2$ or Trial B slope $= 18$ on $KE$ vs. $m$.
Identify which trial has higher speed: Trial A slope $= 2$ or Trial B slope $= 18$ on $KE$ vs. $m$.
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Trial B. Larger slope means larger $\frac{1}{2}v^2$, so higher speed.
Trial B. Larger slope means larger $\frac{1}{2}v^2$, so higher speed.
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Interpret a point on a $KE$ vs. $m$ graph: if $m = 6$ and $KE = 24$, what is slope $\frac{KE}{m}$?
Interpret a point on a $KE$ vs. $m$ graph: if $m = 6$ and $KE = 24$, what is slope $\frac{KE}{m}$?
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Slope $= 4$. Slope equals $\frac{KE}{m} = \frac{24}{6} = 4$.
Slope $= 4$. Slope equals $\frac{KE}{m} = \frac{24}{6} = 4$.
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Identify the pattern: at constant $v$, if $m$ increases by $5$ kg, how does $KE$ change on a linear graph?
Identify the pattern: at constant $v$, if $m$ increases by $5$ kg, how does $KE$ change on a linear graph?
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$KE$ increases by a constant amount each $5$ kg step. Linear relationship means equal increments in $m$ produce equal increments in $KE$.
$KE$ increases by a constant amount each $5$ kg step. Linear relationship means equal increments in $m$ produce equal increments in $KE$.
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A graph shows $KE=20,\text{J}$ at $m=2,\text{kg}$ and constant $v$. What is $KE$ at $m=5,\text{kg}$?
A graph shows $KE=20,\text{J}$ at $m=2,\text{kg}$ and constant $v$. What is $KE$ at $m=5,\text{kg}$?
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$50,\text{J}$. Since $KE \propto m$: $\frac{20}{2} = \frac{KE}{5}$, so $KE = 50,\text{J}$.
$50,\text{J}$. Since $KE \propto m$: $\frac{20}{2} = \frac{KE}{5}$, so $KE = 50,\text{J}$.
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Identify the meaning of a $KE$ vs. $m$ graph that passes through $(0,0)$.
Identify the meaning of a $KE$ vs. $m$ graph that passes through $(0,0)$.
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Zero mass corresponds to zero kinetic energy. No mass means no matter to have kinetic energy.
Zero mass corresponds to zero kinetic energy. No mass means no matter to have kinetic energy.
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If a $KE$ vs. $m$ graph has a nonzero $y$-intercept, what is the likely conclusion?
If a $KE$ vs. $m$ graph has a nonzero $y$-intercept, what is the likely conclusion?
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There is an offset or measurement error. Theory predicts $(0,0)$; nonzero intercept suggests systematic error.
There is an offset or measurement error. Theory predicts $(0,0)$; nonzero intercept suggests systematic error.
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A data table shows constant $v$: $(m,KE)=(1,6),(2,12),(3,18)$. Identify the relationship between $KE$ and $m$.
A data table shows constant $v$: $(m,KE)=(1,6),(2,12),(3,18)$. Identify the relationship between $KE$ and $m$.
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$KE=6m$. Each point shows $KE$ is 6 times $m$.
$KE=6m$. Each point shows $KE$ is 6 times $m$.
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A plot uses $m$ on the $x$-axis and $KE$ on the $y$-axis. What does a proportional pattern look like?
A plot uses $m$ on the $x$-axis and $KE$ on the $y$-axis. What does a proportional pattern look like?
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A straight line through the origin. Proportional relationships graph as lines through the origin.
A straight line through the origin. Proportional relationships graph as lines through the origin.
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Identify the units of the slope on a $KE$ (J) vs. $m$ (kg) graph.
Identify the units of the slope on a $KE$ (J) vs. $m$ (kg) graph.
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$\text{J/kg}$. Slope is $\frac{\Delta KE}{\Delta m} = \frac{\text{J}}{\text{kg}}$.
$\text{J/kg}$. Slope is $\frac{\Delta KE}{\Delta m} = \frac{\text{J}}{\text{kg}}$.
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A $KE$ vs. $m$ line has slope $18,\text{J/kg}$. Identify the speed $v$ using $\text{slope}=\frac{1}{2}v^2$.
A $KE$ vs. $m$ line has slope $18,\text{J/kg}$. Identify the speed $v$ using $\text{slope}=\frac{1}{2}v^2$.
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$v=6,\text{m/s}$. $18 = \frac{1}{2}v^2$ gives $v^2 = 36$, so $v = 6,\text{m/s}$.
$v=6,\text{m/s}$. $18 = \frac{1}{2}v^2$ gives $v^2 = 36$, so $v = 6,\text{m/s}$.
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