Compare Potential Energy - Middle School Physical Science
Card 1 of 25
Identify the relationship between $U_g$ and height $h$ when $m$ and $g$ are constant.
Identify the relationship between $U_g$ and height $h$ when $m$ and $g$ are constant.
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$U_g$ is directly proportional to $h$. When mass and gravity are constant, $U_g$ increases linearly with height.
$U_g$ is directly proportional to $h$. When mass and gravity are constant, $U_g$ increases linearly with height.
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Which has greater gravitational potential energy: mass $2m$ at height $h$ or mass $m$ at $h$?
Which has greater gravitational potential energy: mass $2m$ at height $h$ or mass $m$ at $h$?
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Mass $2m$ at $h$ has greater $U_g$. Doubling mass doubles gravitational potential energy.
Mass $2m$ at $h$ has greater $U_g$. Doubling mass doubles gravitational potential energy.
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Which arrangement has more $U_s$: $k=100,\text{N/m}$, $x=0.10,\text{m}$ or $k=50,\text{N/m}$, $x=0.10,\text{m}$?
Which arrangement has more $U_s$: $k=100,\text{N/m}$, $x=0.10,\text{m}$ or $k=50,\text{N/m}$, $x=0.10,\text{m}$?
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$k=100,\text{N/m}$ case has more $U_s$. Stiffer spring ($k=100$) stores twice the energy at same stretch.
$k=100,\text{N/m}$ case has more $U_s$. Stiffer spring ($k=100$) stores twice the energy at same stretch.
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Which arrangement has more $U_g$: object A at $h=3,\text{m}$ or object B at $h=1,\text{m}$ (same $m$)?
Which arrangement has more $U_g$: object A at $h=3,\text{m}$ or object B at $h=1,\text{m}$ (same $m$)?
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Object A at $3,\text{m}$ has more $U_g$. Higher position means greater gravitational potential energy.
Object A at $3,\text{m}$ has more $U_g$. Higher position means greater gravitational potential energy.
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What is gravitational potential energy in terms of $m$, $g$, and height $h$?
What is gravitational potential energy in terms of $m$, $g$, and height $h$?
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$U_g = mgh$. Formula shows $U_g$ depends on mass, gravity, and height.
$U_g = mgh$. Formula shows $U_g$ depends on mass, gravity, and height.
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What is elastic potential energy in a spring in terms of $k$ and stretch $x$?
What is elastic potential energy in a spring in terms of $k$ and stretch $x$?
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$U_s = \frac{1}{2}kx^2$. Energy stored in spring depends on stiffness $k$ and displacement squared.
$U_s = \frac{1}{2}kx^2$. Energy stored in spring depends on stiffness $k$ and displacement squared.
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Which has greater gravitational potential energy: same mass at $2h$ or at $h$?
Which has greater gravitational potential energy: same mass at $2h$ or at $h$?
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Same mass at $2h$ has greater $U_g$. Doubling height doubles gravitational potential energy.
Same mass at $2h$ has greater $U_g$. Doubling height doubles gravitational potential energy.
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What happens to $U_g$ if an object is moved downward by a height change of $-\Delta h$?
What happens to $U_g$ if an object is moved downward by a height change of $-\Delta h$?
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$U_g$ decreases by $mg\Delta h$. Moving down reduces height, decreasing potential energy.
$U_g$ decreases by $mg\Delta h$. Moving down reduces height, decreasing potential energy.
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Which has greater spring potential energy: spring with $k$ or with $2k$ at the same stretch $x$?
Which has greater spring potential energy: spring with $k$ or with $2k$ at the same stretch $x$?
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Spring with $2k$ has greater $U_s$. Stiffer spring stores more energy at same stretch.
Spring with $2k$ has greater $U_s$. Stiffer spring stores more energy at same stretch.
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Identify the relationship between spring potential energy $U_s$ and stretch $x$ when $k$ is constant.
Identify the relationship between spring potential energy $U_s$ and stretch $x$ when $k$ is constant.
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$U_s$ is proportional to $x^2$. Doubling stretch quadruples spring potential energy.
$U_s$ is proportional to $x^2$. Doubling stretch quadruples spring potential energy.
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Which statement is correct about comparing $U_g$ values if the same zero height is used for both cases?
Which statement is correct about comparing $U_g$ values if the same zero height is used for both cases?
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Higher position means greater $U_g$ for the same $m$. With same reference, higher objects have more $U_g$.
Higher position means greater $U_g$ for the same $m$. With same reference, higher objects have more $U_g$.
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Which system arrangement stores more elastic potential energy: compressed spring by $x$ or uncompressed spring?
Which system arrangement stores more elastic potential energy: compressed spring by $x$ or uncompressed spring?
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Compressed by $x$ stores more $U_s$. Any deformation from equilibrium stores elastic potential energy.
Compressed by $x$ stores more $U_s$. Any deformation from equilibrium stores elastic potential energy.
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Identify which energy depends on position in a gravitational field: kinetic energy or gravitational potential energy.
Identify which energy depends on position in a gravitational field: kinetic energy or gravitational potential energy.
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Gravitational potential energy. Only gravitational PE depends on vertical position.
Gravitational potential energy. Only gravitational PE depends on vertical position.
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Choose the correct comparison: same $m$ and $h$, but larger $g$ versus smaller $g$ for $U_g$.
Choose the correct comparison: same $m$ and $h$, but larger $g$ versus smaller $g$ for $U_g$.
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Larger $g$ gives larger $U_g$. Stronger gravity field increases potential energy at same height.
Larger $g$ gives larger $U_g$. Stronger gravity field increases potential energy at same height.
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Which arrangement has greater total gravitational potential energy: two identical masses each at height $h$ or one identical mass at height $h$?
Which arrangement has greater total gravitational potential energy: two identical masses each at height $h$ or one identical mass at height $h$?
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Two identical masses each at $h$ have greater total $U_g$. Total $U_g = 2(mgh)$ for two masses vs $mgh$ for one.
Two identical masses each at $h$ have greater total $U_g$. Total $U_g = 2(mgh)$ for two masses vs $mgh$ for one.
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Which arrangement has greater $U_s$: spring compressed by $x$ or stretched by $x$ (same $k$)?
Which arrangement has greater $U_s$: spring compressed by $x$ or stretched by $x$ (same $k$)?
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They are equal: both have $U_s = \frac{1}{2}kx^2$. $U_s$ depends on $x^2$, so direction doesn't matter.
They are equal: both have $U_s = \frac{1}{2}kx^2$. $U_s$ depends on $x^2$, so direction doesn't matter.
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Which option has greater elastic potential energy: spring stretched $x=0.10\text{ m}$ or $x=0.20\text{ m}$ (same $k$)?
Which option has greater elastic potential energy: spring stretched $x=0.10\text{ m}$ or $x=0.20\text{ m}$ (same $k$)?
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$x=0.20\text{ m}$ has greater $U_s$. Since $U_s \propto x^2$, larger stretch stores more energy.
$x=0.20\text{ m}$ has greater $U_s$. Since $U_s \propto x^2$, larger stretch stores more energy.
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What is the key condition for a spring to have elastic potential energy in a system?
What is the key condition for a spring to have elastic potential energy in a system?
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It has $U_s$ when it is stretched or compressed from equilibrium. Displacement from equilibrium stores elastic energy in the spring.
It has $U_s$ when it is stretched or compressed from equilibrium. Displacement from equilibrium stores elastic energy in the spring.
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Which position has greater $U_g$: a book on a top shelf or the same book on the floor (same reference)?
Which position has greater $U_g$: a book on a top shelf or the same book on the floor (same reference)?
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The book on the top shelf has greater $U_g$. Higher position means greater height $h$ in $U_g = mgh$.
The book on the top shelf has greater $U_g$. Higher position means greater height $h$ in $U_g = mgh$.
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What is the key condition for an object to have gravitational potential energy in a system?
What is the key condition for an object to have gravitational potential energy in a system?
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It has $U_g$ when it is at a height in a gravitational field. Height above a reference point creates gravitational potential energy.
It has $U_g$ when it is at a height in a gravitational field. Height above a reference point creates gravitational potential energy.
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For the same stretch $x$, which stores more elastic potential energy: spring with $2k$ or spring with $k$?
For the same stretch $x$, which stores more elastic potential energy: spring with $2k$ or spring with $k$?
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The spring with $2k$ stores more $U_s$. $U_s$ is directly proportional to spring constant $k$.
The spring with $2k$ stores more $U_s$. $U_s$ is directly proportional to spring constant $k$.
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Which has greater gravitational potential energy: mass $2m$ at height $h$ or mass $m$ at height $h$?
Which has greater gravitational potential energy: mass $2m$ at height $h$ or mass $m$ at height $h$?
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Mass $2m$ at $h$ has greater $U_g$. Since $U_g = mgh$, doubling mass doubles the potential energy.
Mass $2m$ at $h$ has greater $U_g$. Since $U_g = mgh$, doubling mass doubles the potential energy.
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Which arrangement has greater total potential energy: a spring at $x=0$ and object at $h$ or the same spring at $x\neq 0$ and object at $h$?
Which arrangement has greater total potential energy: a spring at $x=0$ and object at $h$ or the same spring at $x\neq 0$ and object at $h$?
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The arrangement with $x\neq 0$ has greater total potential energy. Stretched/compressed spring adds $U_s > 0$ to the system's total.
The arrangement with $x\neq 0$ has greater total potential energy. Stretched/compressed spring adds $U_s > 0$ to the system's total.
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Which statement is correct about comparing $U_g$ values between two objects?
Which statement is correct about comparing $U_g$ values between two objects?
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Only differences in $U_g$ are physically meaningful. Absolute values depend on reference choice; only changes matter physically.
Only differences in $U_g$ are physically meaningful. Absolute values depend on reference choice; only changes matter physically.
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What reference choice determines whether gravitational potential energy is positive, negative, or zero?
What reference choice determines whether gravitational potential energy is positive, negative, or zero?
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The selected zero-height (reference level). Height is measured from a chosen reference point where $h = 0$.
The selected zero-height (reference level). Height is measured from a chosen reference point where $h = 0$.
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