Design Momentum Conservation Experiments - Physics
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Which collision type is easiest to test for momentum conservation using carts that stick together?
Which collision type is easiest to test for momentum conservation using carts that stick together?
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Perfectly inelastic collision (carts stick; share one final velocity). Single final velocity simplifies analysis.
Perfectly inelastic collision (carts stick; share one final velocity). Single final velocity simplifies analysis.
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What equation defines linear momentum for a single object?
What equation defines linear momentum for a single object?
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$\vec{p}=m\vec{v}$. Momentum equals mass times velocity vector.
$\vec{p}=m\vec{v}$. Momentum equals mass times velocity vector.
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What condition must be met for momentum to be conserved in an experiment?
What condition must be met for momentum to be conserved in an experiment?
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Net external impulse is zero, $\sum J_{ext}=0$ (isolated system). No external forces means no external impulse to change total momentum.
Net external impulse is zero, $\sum J_{ext}=0$ (isolated system). No external forces means no external impulse to change total momentum.
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What conservation equation should you test for a two-cart interaction in 1D?
What conservation equation should you test for a two-cart interaction in 1D?
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$m_1v_{1i}+m_2v_{2i}=m_1v_{1f}+m_2v_{2f}$. Total momentum before equals total momentum after for two objects.
$m_1v_{1i}+m_2v_{2i}=m_1v_{1f}+m_2v_{2f}$. Total momentum before equals total momentum after for two objects.
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Which track setup best reduces external forces when testing cart momentum conservation?
Which track setup best reduces external forces when testing cart momentum conservation?
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Level, low-friction track (or air track) with minimal contact friction. Minimizes external forces that would violate conservation.
Level, low-friction track (or air track) with minimal contact friction. Minimizes external forces that would violate conservation.
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Which measurement tool directly provides cart velocity for momentum tests on a track?
Which measurement tool directly provides cart velocity for momentum tests on a track?
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Photogate(s) with a flag of known length (or motion sensor). Time through flag gives velocity; motion sensors measure directly.
Photogate(s) with a flag of known length (or motion sensor). Time through flag gives velocity; motion sensors measure directly.
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What quantities must you measure to compute total momentum before and after a collision?
What quantities must you measure to compute total momentum before and after a collision?
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Each cart mass $m$ and velocity $v$ before and after the interaction. Need all masses and velocities to calculate $p=mv$ for each object.
Each cart mass $m$ and velocity $v$ before and after the interaction. Need all masses and velocities to calculate $p=mv$ for each object.
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Which variable should you keep constant to isolate the effect of mass on momentum conservation results?
Which variable should you keep constant to isolate the effect of mass on momentum conservation results?
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Track conditions (levelness and friction) and the collision mechanism. Controls ensure only mass variation affects results.
Track conditions (levelness and friction) and the collision mechanism. Controls ensure only mass variation affects results.
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What is the independent variable in a design where you change cart masses and test conservation?
What is the independent variable in a design where you change cart masses and test conservation?
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Cart mass configuration (values of $m_1$ and/or $m_2$). You manipulate mass to see its effect on conservation.
Cart mass configuration (values of $m_1$ and/or $m_2$). You manipulate mass to see its effect on conservation.
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What is the dependent variable when testing whether total momentum is conserved?
What is the dependent variable when testing whether total momentum is conserved?
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Difference between totals: $\Delta p=p_f-p_i$ (or percent difference). Measures how well momentum is conserved.
Difference between totals: $\Delta p=p_f-p_i$ (or percent difference). Measures how well momentum is conserved.
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What calculation gives the percent difference used to judge momentum conservation?
What calculation gives the percent difference used to judge momentum conservation?
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$%\text{diff}=\frac{|p_f-p_i|}{|p_i|}\times 100%$. Normalizes difference by initial value for comparison.
$%\text{diff}=\frac{|p_f-p_i|}{|p_i|}\times 100%$. Normalizes difference by initial value for comparison.
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Which sign convention should you state when measuring 1D velocities for momentum calculations?
Which sign convention should you state when measuring 1D velocities for momentum calculations?
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Choose + direction along the track; opposite motion has negative $v$. Ensures consistent velocity signs for momentum calculations.
Choose + direction along the track; opposite motion has negative $v$. Ensures consistent velocity signs for momentum calculations.
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Identify the best control to check for external impulse before running collisions.
Identify the best control to check for external impulse before running collisions.
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Verify constant velocity for a single cart: $\Delta v\approx 0$ over time. No velocity change confirms negligible external forces.
Verify constant velocity for a single cart: $\Delta v\approx 0$ over time. No velocity change confirms negligible external forces.
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Find the total initial momentum if $m_1=0.50,\text{kg}$ at $+0.80,\text{m/s}$ and $m_2=0.50,\text{kg}$ at $-0.20,\text{m/s}$.
Find the total initial momentum if $m_1=0.50,\text{kg}$ at $+0.80,\text{m/s}$ and $m_2=0.50,\text{kg}$ at $-0.20,\text{m/s}$.
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$p_i=0.30,\text{kg}\cdot\text{m/s}$. $p_i=(0.50)(0.80)+(0.50)(-0.20)=0.40-0.10=0.30$
$p_i=0.30,\text{kg}\cdot\text{m/s}$. $p_i=(0.50)(0.80)+(0.50)(-0.20)=0.40-0.10=0.30$
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Find $p_f$ if $m_1=0.40,\text{kg}$ at $+0.25,\text{m/s}$ and $m_2=0.60,\text{kg}$ at $+0.10,\text{m/s}$ after collision.
Find $p_f$ if $m_1=0.40,\text{kg}$ at $+0.25,\text{m/s}$ and $m_2=0.60,\text{kg}$ at $+0.10,\text{m/s}$ after collision.
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$p_f=0.16,\text{kg}\cdot\text{m/s}$. $p_f=(0.40)(0.25)+(0.60)(0.10)=0.10+0.06=0.16$
$p_f=0.16,\text{kg}\cdot\text{m/s}$. $p_f=(0.40)(0.25)+(0.60)(0.10)=0.10+0.06=0.16$
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Compute $%\text{diff}$ if $p_i=0.50$ and $p_f=0.47$ in $\text{kg}\cdot\text{m/s}$.
Compute $%\text{diff}$ if $p_i=0.50$ and $p_f=0.47$ in $\text{kg}\cdot\text{m/s}$.
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$6%$. $%\text{diff}=\frac{|0.47-0.50|}{0.50}\times 100%=6%$
$6%$. $%\text{diff}=\frac{|0.47-0.50|}{0.50}\times 100%=6%$
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Identify the missing step: you used photogates but did not know cart speed; what must be measured?
Identify the missing step: you used photogates but did not know cart speed; what must be measured?
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Flag length $L$ to compute $v=\frac{L}{\Delta t}$. Photogate timing gives $\Delta t$; need $L$ for velocity.
Flag length $L$ to compute $v=\frac{L}{\Delta t}$. Photogate timing gives $\Delta t$; need $L$ for velocity.
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Which option best reduces the effect of a small constant friction force during the collision interval?
Which option best reduces the effect of a small constant friction force during the collision interval?
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Use a short collision time and measure velocities immediately before and after. Minimizes impulse from friction during collision.
Use a short collision time and measure velocities immediately before and after. Minimizes impulse from friction during collision.
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What graph would best show whether $p_f$ matches $p_i$ across many trials of different masses?
What graph would best show whether $p_f$ matches $p_i$ across many trials of different masses?
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Scatter plot of $p_f$ vs $p_i$; ideal trend is $p_f=p_i$ (slope $1$). Perfect conservation shows as 45° line through origin.
Scatter plot of $p_f$ vs $p_i$; ideal trend is $p_f=p_i$ (slope $1$). Perfect conservation shows as 45° line through origin.
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Which diagram best represents a 1D two-cart collision experiment used to test momentum conservation?
Which diagram best represents a 1D two-cart collision experiment used to test momentum conservation?
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Two carts on a straight track with labeled $m_1,m_2$ and $v_{1i},v_{2i},v_{1f},v_{2f}$. Shows all needed quantities for momentum calculations.
Two carts on a straight track with labeled $m_1,m_2$ and $v_{1i},v_{2i},v_{1f},v_{2f}$. Shows all needed quantities for momentum calculations.
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Find $p_f$ for $m_1=0.50,\text{kg}$, $v_{1f}=0.20,\text{m/s}$, $m_2=0.30,\text{kg}$, $v_{2f}=1.00,\text{m/s}$.
Find $p_f$ for $m_1=0.50,\text{kg}$, $v_{1f}=0.20,\text{m/s}$, $m_2=0.30,\text{kg}$, $v_{2f}=1.00,\text{m/s}$.
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$p_f=0.40,\text{kg}\cdot\text{m/s}$. $p_f = (0.50)(0.20) + (0.30)(1.00) = 0.10 + 0.30 = 0.40,\text{kg}\cdot\text{m/s}$
$p_f=0.40,\text{kg}\cdot\text{m/s}$. $p_f = (0.50)(0.20) + (0.30)(1.00) = 0.10 + 0.30 = 0.40,\text{kg}\cdot\text{m/s}$
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Choose the correct conclusion: if $p_i=0.60$ and $p_f=0.58,\text{kg}\cdot\text{m/s}$ with small uncertainty, is momentum conserved?
Choose the correct conclusion: if $p_i=0.60$ and $p_f=0.58,\text{kg}\cdot\text{m/s}$ with small uncertainty, is momentum conserved?
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Yes, within experimental uncertainty ($p_f\approx p_i$). $3.3%$ difference is within typical experimental error.
Yes, within experimental uncertainty ($p_f\approx p_i$). $3.3%$ difference is within typical experimental error.
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Which design change best reduces external impulse in a cart collision: add a fan, add magnets, or level the track?
Which design change best reduces external impulse in a cart collision: add a fan, add magnets, or level the track?
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Level the track (minimizes external force component along motion). Eliminates gravity component along track, unlike fans or magnets which add forces.
Level the track (minimizes external force component along motion). Eliminates gravity component along track, unlike fans or magnets which add forces.
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Which measurement tools are most appropriate to obtain cart velocities in a momentum lab?
Which measurement tools are most appropriate to obtain cart velocities in a momentum lab?
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Photogates or motion sensor (or video analysis with scale). These tools measure velocity precisely without disturbing the motion.
Photogates or motion sensor (or video analysis with scale). These tools measure velocity precisely without disturbing the motion.
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What should be defined as the system when testing momentum conservation in a cart collision?
What should be defined as the system when testing momentum conservation in a cart collision?
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Both carts (and any attached masses) treated as one system. System boundary must include all interacting objects for conservation to apply.
Both carts (and any attached masses) treated as one system. System boundary must include all interacting objects for conservation to apply.
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State the momentum conservation equation for two objects in one dimension.
State the momentum conservation equation for two objects in one dimension.
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$m_1v_{1i}+m_2v_{2i}=m_1v_{1f}+m_2v_{2f}$. Total momentum before equals total momentum after in isolated systems.
$m_1v_{1i}+m_2v_{2i}=m_1v_{1f}+m_2v_{2f}$. Total momentum before equals total momentum after in isolated systems.
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What is the vector definition of linear momentum for an object used in conservation tests?
What is the vector definition of linear momentum for an object used in conservation tests?
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$\vec{p}=m\vec{v}$. Momentum is mass times velocity, both magnitude and direction matter.
$\vec{p}=m\vec{v}$. Momentum is mass times velocity, both magnitude and direction matter.
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What condition must be met for a collision experiment to test momentum conservation in a system?
What condition must be met for a collision experiment to test momentum conservation in a system?
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Net external impulse is negligible: $\sum \vec{F}_{ext}\Delta t \approx 0$. External forces must be minimal during collision time for momentum to be conserved.
Net external impulse is negligible: $\sum \vec{F}_{ext}\Delta t \approx 0$. External forces must be minimal during collision time for momentum to be conserved.
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What is the best operational check that a track is level before momentum trials?
What is the best operational check that a track is level before momentum trials?
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A cart at rest remains at rest (no drift) on the track. No drift indicates zero net force along track direction.
A cart at rest remains at rest (no drift) on the track. No drift indicates zero net force along track direction.
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Which variable should be controlled to reduce external forces in a cart collision test?
Which variable should be controlled to reduce external forces in a cart collision test?
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Track level and friction (use low-friction track, level it). Minimizing friction and gravity components ensures negligible external forces.
Track level and friction (use low-friction track, level it). Minimizing friction and gravity components ensures negligible external forces.
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