Gravity Depends on Mass - Middle School Physical Science
Card 1 of 25
What happens to $F_g$ if both masses double while distance $r$ stays constant?
What happens to $F_g$ if both masses double while distance $r$ stays constant?
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$F_g$ becomes $4$ times as large. Doubling both masses quadruples their product, quadrupling the force.
$F_g$ becomes $4$ times as large. Doubling both masses quadruples their product, quadrupling the force.
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What happens to $F_g$ if $m_1$ doubles while $m_2$ and $r$ stay constant?
What happens to $F_g$ if $m_1$ doubles while $m_2$ and $r$ stay constant?
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$F_g$ doubles. Force is directly proportional to each mass, so doubling one doubles the force.
$F_g$ doubles. Force is directly proportional to each mass, so doubling one doubles the force.
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What happens to $F_g$ if $m_1$ is halved while $m_2$ and $r$ stay constant?
What happens to $F_g$ if $m_1$ is halved while $m_2$ and $r$ stay constant?
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$F_g$ is halved. Force is directly proportional to $m_1$, so halving it halves the force.
$F_g$ is halved. Force is directly proportional to $m_1$, so halving it halves the force.
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Which relationship between force and mass product is correct when $r$ is constant: $F_g\propto m_1+m_2$ or $F_g\propto m_1m_2$?
Which relationship between force and mass product is correct when $r$ is constant: $F_g\propto m_1+m_2$ or $F_g\propto m_1m_2$?
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$F_g\propto m_1m_2$. Force depends on the product of masses, not their sum.
$F_g\propto m_1m_2$. Force depends on the product of masses, not their sum.
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If the product $m_1m_2$ increases from $10$ to $30$ and $r$ is constant, what happens to $F_g$?
If the product $m_1m_2$ increases from $10$ to $30$ and $r$ is constant, what happens to $F_g$?
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$F_g$ becomes $3$ times as large. Force is proportional to mass product: $30/10 = 3$ times larger.
$F_g$ becomes $3$ times as large. Force is proportional to mass product: $30/10 = 3$ times larger.
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Two trials keep $r$ the same. Trial A has $m_1m_2=12$, Trial B has $m_1m_2=20$. Which trial has larger $F_g$?
Two trials keep $r$ the same. Trial A has $m_1m_2=12$, Trial B has $m_1m_2=20$. Which trial has larger $F_g$?
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Trial B. Larger mass product ($20 > 12$) means larger gravitational force.
Trial B. Larger mass product ($20 > 12$) means larger gravitational force.
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With constant $r$, if $m_1m_2$ is multiplied by $\frac{1}{4}$, what happens to $F_g$?
With constant $r$, if $m_1m_2$ is multiplied by $\frac{1}{4}$, what happens to $F_g$?
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$F_g$ is multiplied by $\frac{1}{4}$. Force scales with mass product, so it's also multiplied by $\frac{1}{4}$.
$F_g$ is multiplied by $\frac{1}{4}$. Force scales with mass product, so it's also multiplied by $\frac{1}{4}$.
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A data table shows $F_g$ stays constant when $r$ is constant but $m_1$ increases. What must happen to $m_2$?
A data table shows $F_g$ stays constant when $r$ is constant but $m_1$ increases. What must happen to $m_2$?
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$m_2$ must decrease in inverse proportion to $m_1$. To keep $m_1m_2$ constant, $m_2$ must decrease as $m_1$ increases.
$m_2$ must decrease in inverse proportion to $m_1$. To keep $m_1m_2$ constant, $m_2$ must decrease as $m_1$ increases.
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If $m_1$ increases by a factor of $5$ and $m_2$ decreases by a factor of $5$ with constant $r$, what happens to $F_g$?
If $m_1$ increases by a factor of $5$ and $m_2$ decreases by a factor of $5$ with constant $r$, what happens to $F_g$?
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$F_g$ stays the same. Mass product remains unchanged: $5m_1 \times \frac{m_2}{5} = m_1m_2$.
$F_g$ stays the same. Mass product remains unchanged: $5m_1 \times \frac{m_2}{5} = m_1m_2$.
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Choose the correct statement for constant $r$: $F_g$ is directly proportional to which quantity?
Choose the correct statement for constant $r$: $F_g$ is directly proportional to which quantity?
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The product $m_1m_2$. At constant distance, gravitational force varies with mass product.
The product $m_1m_2$. At constant distance, gravitational force varies with mass product.
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A graph plots $F_g$ versus $m_1$ with $m_2$ and $r$ constant. What is the expected graph shape?
A graph plots $F_g$ versus $m_1$ with $m_2$ and $r$ constant. What is the expected graph shape?
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A straight line through the origin. Direct proportionality creates a linear relationship passing through origin.
A straight line through the origin. Direct proportionality creates a linear relationship passing through origin.
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A graph plots $F_g$ versus $m_1m_2$ with constant $r$. What is the expected relationship?
A graph plots $F_g$ versus $m_1m_2$ with constant $r$. What is the expected relationship?
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Linear: $F_g$ increases directly with $m_1m_2$. Direct proportionality means force increases linearly with mass product.
Linear: $F_g$ increases directly with $m_1m_2$. Direct proportionality means force increases linearly with mass product.
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If $F_g$ is $12\ \text{N}$ for masses $m_1$ and $m_2$ at fixed $r$, what is $F_g$ when $m_2$ becomes $3m_2$?
If $F_g$ is $12\ \text{N}$ for masses $m_1$ and $m_2$ at fixed $r$, what is $F_g$ when $m_2$ becomes $3m_2$?
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$36\ \text{N}$. Tripling one mass triples the force: $3 \times 12 = 36$ N.
$36\ \text{N}$. Tripling one mass triples the force: $3 \times 12 = 36$ N.
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If $F_g$ is $40\ \text{N}$ at fixed $r$, what is the new $F_g$ when $m_1$ becomes $\frac{1}{2}m_1$ and $m_2$ becomes $2m_2$?
If $F_g$ is $40\ \text{N}$ at fixed $r$, what is the new $F_g$ when $m_1$ becomes $\frac{1}{2}m_1$ and $m_2$ becomes $2m_2$?
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$40\ \text{N}$. Mass product unchanged: $\frac{1}{2} \times 2 = 1$, so force stays same.
$40\ \text{N}$. Mass product unchanged: $\frac{1}{2} \times 2 = 1$, so force stays same.
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Two experiments keep $r$ constant. Exp 1: $m_1=2$, $m_2=6$. Exp 2: $m_1=3$, $m_2=4$. Which has larger $F_g$?
Two experiments keep $r$ constant. Exp 1: $m_1=2$, $m_2=6$. Exp 2: $m_1=3$, $m_2=4$. Which has larger $F_g$?
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They are equal. Both have same mass product: $2 \times 6 = 3 \times 4 = 12$.
They are equal. Both have same mass product: $2 \times 6 = 3 \times 4 = 12$.
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Identify the correct conclusion: If $m_1$ is $10$ times $m_2$ at the same $r$, which force is larger, on $m_1$ or on $m_2$?
Identify the correct conclusion: If $m_1$ is $10$ times $m_2$ at the same $r$, which force is larger, on $m_1$ or on $m_2$?
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Neither; the forces are equal in magnitude. Newton's third law: gravitational forces are equal and opposite pairs.
Neither; the forces are equal in magnitude. Newton's third law: gravitational forces are equal and opposite pairs.
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What happens to $F_g$ if $m_1$ is tripled while $m_2$ and $r$ stay constant?
What happens to $F_g$ if $m_1$ is tripled while $m_2$ and $r$ stay constant?
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$F_g$ triples. Force is directly proportional to $m_1$, so tripling it triples the force.
$F_g$ triples. Force is directly proportional to $m_1$, so tripling it triples the force.
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If both masses double (same $r$), by what factor does $F_g$ change?
If both masses double (same $r$), by what factor does $F_g$ change?
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$F_g$ increases by a factor of $4$. Doubling both masses quadruples their product $m_1m_2$.
$F_g$ increases by a factor of $4$. Doubling both masses quadruples their product $m_1m_2$.
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Two trials have the same $r$. Trial A has $(m_1,m_2)=(2,3)$ and Trial B has $(m_1,m_2)=(1,12)$. Which has larger $F_g$?
Two trials have the same $r$. Trial A has $(m_1,m_2)=(2,3)$ and Trial B has $(m_1,m_2)=(1,12)$. Which has larger $F_g$?
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Trial B (product $m_1m_2$ is larger). Compare products: $2 \times 3 = 6$ vs $1 \times 12 = 12$.
Trial B (product $m_1m_2$ is larger). Compare products: $2 \times 3 = 6$ vs $1 \times 12 = 12$.
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If a graph of $F_g$ versus $m_1m_2$ is linear through the origin (constant $r$), what is the conclusion?
If a graph of $F_g$ versus $m_1m_2$ is linear through the origin (constant $r$), what is the conclusion?
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$F_g \propto m_1m_2$ when $r$ is constant. Linear graph through origin confirms direct proportionality.
$F_g \propto m_1m_2$ when $r$ is constant. Linear graph through origin confirms direct proportionality.
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A table shows $m_1$ doubles and $F_g$ quadruples (same $r$). Which mass change must also have occurred?
A table shows $m_1$ doubles and $F_g$ quadruples (same $r$). Which mass change must also have occurred?
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$m_2$ also doubled. Quadrupling force with doubled $m_1$ means $m_2$ also doubled.
$m_2$ also doubled. Quadrupling force with doubled $m_1$ means $m_2$ also doubled.
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What does it mean if data show $F_g$ doubles when $m_1$ doubles (same $m_2,r$)?
What does it mean if data show $F_g$ doubles when $m_1$ doubles (same $m_2,r$)?
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$F_g \propto m_1$ for constant $m_2$ and $r$. Direct proportionality means force scales linearly with mass.
$F_g \propto m_1$ for constant $m_2$ and $r$. Direct proportionality means force scales linearly with mass.
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Identify the relationship shown by a straight-line graph of $F_g$ versus $m_1$ when $m_2$ and $r$ are constant.
Identify the relationship shown by a straight-line graph of $F_g$ versus $m_1$ when $m_2$ and $r$ are constant.
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Directly proportional (linear through the origin). Straight line through origin indicates direct proportionality.
Directly proportional (linear through the origin). Straight line through origin indicates direct proportionality.
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What is the ratio $\frac{F_2}{F_1}$ if masses change to $(\frac{1}{4}m_1,4m_2)$ with the same $r$?
What is the ratio $\frac{F_2}{F_1}$ if masses change to $(\frac{1}{4}m_1,4m_2)$ with the same $r$?
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$\frac{F_2}{F_1}=1$. Product remains same: $\frac{1}{4}m_1 \times 4m_2 = m_1m_2$.
$\frac{F_2}{F_1}=1$. Product remains same: $\frac{1}{4}m_1 \times 4m_2 = m_1m_2$.
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What is the ratio $\frac{F_2}{F_1}$ if $m_1$ changes from $m_1$ to $3m_1$ (same $m_2,r$)?
What is the ratio $\frac{F_2}{F_1}$ if $m_1$ changes from $m_1$ to $3m_1$ (same $m_2,r$)?
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$\frac{F_2}{F_1}=3$. Tripling one mass triples the force proportionally.
$\frac{F_2}{F_1}=3$. Tripling one mass triples the force proportionally.
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