Graph Energy and Mass - Middle School Physical Science
Card 1 of 25
If $v$ is constant, what is the slope of a $KE$ vs. $m$ graph in terms of $v$?
If $v$ is constant, what is the slope of a $KE$ vs. $m$ graph in terms of $v$?
Tap to reveal answer
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.
← Didn't Know|Knew It →
What is the kinetic energy formula for an object of mass $m$ moving at speed $v$?
What is the kinetic energy formula for an object of mass $m$ moving at speed $v$?
Tap to reveal answer
$KE = \frac{1}{2}mv^2$. Energy equals half the product of mass and velocity squared.
$KE = \frac{1}{2}mv^2$. Energy equals half the product of mass and velocity squared.
← Didn't Know|Knew It →
What variable should be on the $x$-axis to graph how $KE$ changes with mass at constant speed?
What variable should be on the $x$-axis to graph how $KE$ changes with mass at constant speed?
Tap to reveal answer
Mass, $m$. Independent variable goes on horizontal axis when graphing relationships.
Mass, $m$. Independent variable goes on horizontal axis when graphing relationships.
← Didn't Know|Knew It →
What variable should be on the $y$-axis to graph how kinetic energy changes with mass?
What variable should be on the $y$-axis to graph how kinetic energy changes with mass?
Tap to reveal answer
Kinetic energy, $KE$. Dependent variable goes on vertical axis to show how it changes.
Kinetic energy, $KE$. Dependent variable goes on vertical axis to show how it changes.
← Didn't Know|Knew It →
What is the expected graph shape of $KE$ vs. $m$ when speed $v$ is constant?
What is the expected graph shape of $KE$ vs. $m$ when speed $v$ is constant?
Tap to reveal answer
A straight line (linear increase). Since $KE = \frac{1}{2}mv^2$ and $v$ is constant, $KE$ increases linearly with $m$.
A straight line (linear increase). Since $KE = \frac{1}{2}mv^2$ and $v$ is constant, $KE$ increases linearly with $m$.
← Didn't Know|Knew It →
If $v$ is constant, what is the proportional relationship between $KE$ and mass $m$?
If $v$ is constant, what is the proportional relationship between $KE$ and mass $m$?
Tap to reveal answer
$KE \propto m$. Direct proportionality since $KE = \frac{1}{2}mv^2$ with constant $v$.
$KE \propto m$. Direct proportionality since $KE = \frac{1}{2}mv^2$ with constant $v$.
← Didn't Know|Knew It →
If $v$ is constant, what is the $y$-intercept of a $KE$ vs. $m$ graph (ideal model)?
If $v$ is constant, what is the $y$-intercept of a $KE$ vs. $m$ graph (ideal model)?
Tap to reveal answer
$0$ (passes through the origin). When $m = 0$, $KE = 0$, so the line passes through the origin.
$0$ (passes through the origin). When $m = 0$, $KE = 0$, so the line passes through the origin.
← Didn't Know|Knew It →
Identify the correct unit for kinetic energy to label the $y$-axis on a graph.
Identify the correct unit for kinetic energy to label the $y$-axis on a graph.
Tap to reveal answer
Joules, $J$. SI unit for energy, where $1,J = 1,kg \cdot m^2/s^2$.
Joules, $J$. SI unit for energy, where $1,J = 1,kg \cdot m^2/s^2$.
← Didn't Know|Knew It →
Identify the correct unit for mass to label the $x$-axis on a graph.
Identify the correct unit for mass to label the $x$-axis on a graph.
Tap to reveal answer
Kilograms, $kg$. SI base unit for mass in the metric system.
Kilograms, $kg$. SI base unit for mass in the metric system.
← Didn't Know|Knew It →
What happens to $KE$ if mass doubles while speed stays constant?
What happens to $KE$ if mass doubles while speed stays constant?
Tap to reveal answer
$KE$ doubles. Direct proportionality means $KE$ scales linearly with mass.
$KE$ doubles. Direct proportionality means $KE$ scales linearly with mass.
← Didn't Know|Knew It →
What happens to $KE$ if mass triples while speed stays constant?
What happens to $KE$ if mass triples while speed stays constant?
Tap to reveal answer
$KE$ triples. Linear relationship means $KE$ increases by same factor as mass.
$KE$ triples. Linear relationship means $KE$ increases by same factor as mass.
← Didn't Know|Knew It →
Calculate $KE$ for $m = 2,kg$ and $v = 3,m/s$.
Calculate $KE$ for $m = 2,kg$ and $v = 3,m/s$.
Tap to reveal answer
$9,J$. $KE = \frac{1}{2}(2)(3^2) = \frac{1}{2}(2)(9) = 9,J$.
$9,J$. $KE = \frac{1}{2}(2)(3^2) = \frac{1}{2}(2)(9) = 9,J$.
← Didn't Know|Knew It →
Calculate $KE$ for $m = 4,kg$ and $v = 2,m/s$.
Calculate $KE$ for $m = 4,kg$ and $v = 2,m/s$.
Tap to reveal answer
$8,J$. $KE = \frac{1}{2}(4)(2^2) = \frac{1}{2}(4)(4) = 8,J$.
$8,J$. $KE = \frac{1}{2}(4)(2^2) = \frac{1}{2}(4)(4) = 8,J$.
← Didn't Know|Knew It →
At constant $v = 4,m/s$, what is $KE$ when $m = 3,kg$?
At constant $v = 4,m/s$, what is $KE$ when $m = 3,kg$?
Tap to reveal answer
$24,J$. $KE = \frac{1}{2}(3)(4^2) = \frac{1}{2}(3)(16) = 24,J$.
$24,J$. $KE = \frac{1}{2}(3)(4^2) = \frac{1}{2}(3)(16) = 24,J$.
← Didn't Know|Knew It →
At constant $v = 5,m/s$, what is $KE$ when $m = 2,kg$?
At constant $v = 5,m/s$, what is $KE$ when $m = 2,kg$?
Tap to reveal answer
$25,J$. $KE = \frac{1}{2}(2)(5^2) = \frac{1}{2}(2)(25) = 25,J$.
$25,J$. $KE = \frac{1}{2}(2)(5^2) = \frac{1}{2}(2)(25) = 25,J$.
← Didn't Know|Knew It →
At constant $v = 6,m/s$, what is $KE$ when $m = 0.5,kg$?
At constant $v = 6,m/s$, what is $KE$ when $m = 0.5,kg$?
Tap to reveal answer
$9,J$. $KE = \frac{1}{2}(0.5)(6^2) = \frac{1}{2}(0.5)(36) = 9,J$.
$9,J$. $KE = \frac{1}{2}(0.5)(6^2) = \frac{1}{2}(0.5)(36) = 9,J$.
← Didn't Know|Knew It →
If a $KE$ vs. $m$ graph has slope $8$, what constant speed $v$ does it imply?
If a $KE$ vs. $m$ graph has slope $8$, what constant speed $v$ does it imply?
Tap to reveal answer
$v = 4,m/s$. Since slope $= \frac{1}{2}v^2 = 8$, then $v^2 = 16$, so $v = 4,m/s$.
$v = 4,m/s$. Since slope $= \frac{1}{2}v^2 = 8$, then $v^2 = 16$, so $v = 4,m/s$.
← Didn't Know|Knew It →
If a $KE$ vs. $m$ graph has slope $18$, what constant speed $v$ does it imply?
If a $KE$ vs. $m$ graph has slope $18$, what constant speed $v$ does it imply?
Tap to reveal answer
$v = 6,m/s$. Since slope $= \frac{1}{2}v^2 = 18$, then $v^2 = 36$, so $v = 6,m/s$.
$v = 6,m/s$. Since slope $= \frac{1}{2}v^2 = 18$, then $v^2 = 36$, so $v = 6,m/s$.
← Didn't Know|Knew It →
If $KE = 40,J$ at $m = 5,kg$, what is the constant speed $v$?
If $KE = 40,J$ at $m = 5,kg$, what is the constant speed $v$?
Tap to reveal answer
$v = 4,m/s$. From $40 = \frac{1}{2}(5)v^2$, we get $v^2 = 16$, so $v = 4,m/s$.
$v = 4,m/s$. From $40 = \frac{1}{2}(5)v^2$, we get $v^2 = 16$, so $v = 4,m/s$.
← Didn't Know|Knew It →
Choose the correct point for a $KE$ vs. $m$ graph at $v = 3,m/s$ when $m = 2,kg$.
Choose the correct point for a $KE$ vs. $m$ graph at $v = 3,m/s$ when $m = 2,kg$.
Tap to reveal answer
$(2,,9)$. When $m = 2,kg$ and $v = 3,m/s$, $KE = \frac{1}{2}(2)(9) = 9,J$.
$(2,,9)$. When $m = 2,kg$ and $v = 3,m/s$, $KE = \frac{1}{2}(2)(9) = 9,J$.
← Didn't Know|Knew It →
State the slope of a $KE$ versus $m$ graph when speed $v$ is constant.
State the slope of a $KE$ versus $m$ graph when speed $v$ is constant.
Tap to reveal answer
Slope $=\frac{1}{2}v^2$. From $KE=\frac{1}{2}mv^2$, the coefficient of $m$ is the slope.
Slope $=\frac{1}{2}v^2$. From $KE=\frac{1}{2}mv^2$, the coefficient of $m$ is the slope.
← Didn't Know|Knew It →
If mass doubles while speed $v$ stays constant, how does $KE$ change?
If mass doubles while speed $v$ stays constant, how does $KE$ change?
Tap to reveal answer
$KE$ doubles. Direct proportionality means if $m$ doubles, $KE$ doubles too.
$KE$ doubles. Direct proportionality means if $m$ doubles, $KE$ doubles too.
← Didn't Know|Knew It →
If mass triples while speed $v$ stays constant, how does $KE$ change?
If mass triples while speed $v$ stays constant, how does $KE$ change?
Tap to reveal answer
$KE$ triples. Direct proportionality means if $m$ triples, $KE$ triples too.
$KE$ triples. Direct proportionality means if $m$ triples, $KE$ triples too.
← Didn't Know|Knew It →
Identify the correct plot points for $v=2,\text{m/s}$ at $m=0,1,2,\text{kg}$ on a $KE$ vs $m$ graph.
Identify the correct plot points for $v=2,\text{m/s}$ at $m=0,1,2,\text{kg}$ on a $KE$ vs $m$ graph.
Tap to reveal answer
$(0,0)$, $(1,2)$, $(2,4)$. Using $KE=\frac{1}{2}mv^2$ with $v=2$: $(0,0)$, $(1,2)$, $(2,4)$.
$(0,0)$, $(1,2)$, $(2,4)$. Using $KE=\frac{1}{2}mv^2$ with $v=2$: $(0,0)$, $(1,2)$, $(2,4)$.
← Didn't Know|Knew It →
Choose the correct statement about the graph: at constant $v$, increasing $m$ makes $KE$ increase at a constant rate.
Choose the correct statement about the graph: at constant $v$, increasing $m$ makes $KE$ increase at a constant rate.
Tap to reveal answer
True; the $KE$ vs $m$ graph is linear. Linear relationship means constant rate of change.
True; the $KE$ vs $m$ graph is linear. Linear relationship means constant rate of change.
← Didn't Know|Knew It →