Design Momentum Conservation Experiments - Physics

1. 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 $-0.20\,\text{m/s}$.

   $p_i=0.30\,\text{kg}\cdot\text{m/s}$. $p_i=(0.50)(0.80)+(0.50)(-0.20)=0.40-0.10=0.30$

2. What formula should you use to compute the system momentum before collision in $1\text{D}$?

   $p_i=m_1v_{1i}+m_2v_{2i}$. Sum individual momenta algebraically with proper signs.

3. What is the correct sign convention to specify before collecting momentum data in $1\text{D}$?

   Choose one direction as positive; opposite direction is negative. Sign convention prevents errors when velocities oppose each other.

4. Which collision type is easiest to test for momentum conservation using carts that stick together?

   Perfectly inelastic collision (carts stick; share one final velocity). Single final velocity simplifies analysis.

5. What should be defined as the system when testing momentum conservation in a cart collision?

   Both carts (and any attached masses) treated as one system. System boundary must include all interacting objects for conservation to apply.

6. 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.

   $p_f=0.16\,\text{kg}\cdot\text{m/s}$. $p_f=(0.40)(0.25)+(0.60)(0.10)=0.10+0.06=0.16$

7. What is the best operational check that a track is level before momentum trials?

   A cart at rest remains at rest (no drift) on the track. No drift indicates zero net force along track direction.

8. Which design change best reduces external impulse in a cart collision: add a fan, add magnets, or level the track?

   Level the track (minimizes external force component along motion). Eliminates gravity component along track, unlike fans or magnets which add forces.

9. What quantities must you measure to compute total momentum before and after a collision?

   Each cart mass $m$ and velocity $v$ before and after the interaction. Need all masses and velocities to calculate $p=mv$ for each object.

10. Which variable should be controlled to reduce external forces in a cart collision test?

    Track level and friction (use low-friction track, level it). Minimizing friction and gravity components ensures negligible external forces.

11. Which diagram best represents a 1D two-cart collision experiment used to test momentum conservation?

    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.

12. Find $p_f$ for $m_1=0.50\,\text{kg}$, $v_{1f}=0.20\,\text{m/s}$, $m_2=0.30\,\text{kg}$, $v_{2f}=1.00\,\text{m/s}$.

    $p_f=0.40\,\text{kg}\cdot\text{m/s}$. $p_f = (0.50)(0.20) + (0.30)(1.00) = 0.10 + 0.30 = 0.40\,\text{kg}\cdot\text{m/s}$

13. Which measurement tool directly provides cart velocity for momentum tests on a track?

    Photogate(s) with a flag of known length (or motion sensor). Time through flag gives velocity; motion sensors measure directly.

14. What is the independent variable in a design where you change cart masses and test conservation?

    Cart mass configuration (values of $m_1$ and/or $m_2$). You manipulate mass to see its effect on conservation.

15. 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?

    Yes, within experimental uncertainty ($p_f\approx p_i$). $3.3\%$ difference is within typical experimental error.

16. Which collision type is most suitable for testing momentum conservation with minimal ambiguity?

    One-dimensional head-on collision along a straight track. Simplifies vector analysis to scalar math with sign convention.

17. Which track setup best reduces external forces when testing cart momentum conservation?

    Level, low-friction track (or air track) with minimal contact friction. Minimizes external forces that would violate conservation.

18. Identify the independent variable in a basic momentum-conservation collision experiment design.

    Initial conditions (for example $v_{1i}$ or mass distribution). The experimenter controls what collides and how fast.

19. State the momentum conservation equation for two objects in one dimension.

    $m_1v_{1i}+m_2v_{2i}=m_1v_{1f}+m_2v_{2f}$. Total momentum before equals total momentum after in isolated systems.

20. What equation defines linear momentum for a single object?

    $\vec{p}=m\vec{v}$. Momentum equals mass times velocity vector.

21. Identify the sign of $p$ for a cart moving left if right is defined as positive in $1\text{D}$.

    Negative momentum: $p<0$. Velocity opposite to positive direction has negative sign.

22. Find $p_i$ for $m_1=0.50\,\text{kg}$, $v_{1i}=0.80\,\text{m/s}$, $m_2=0.30\,\text{kg}$, $v_{2i}=0$.

    $p_i=0.40\,\text{kg}\cdot\text{m/s}$. $p_i = (0.50)(0.80) + (0.30)(0) = 0.40\,\text{kg}\cdot\text{m/s}$

23. Identify the dependent variable used to evaluate momentum conservation in the experiment.

    Change in system momentum: $\Delta p=p_f-p_i$ (or percent difference). Measures how well momentum is conserved in the collision.

24. What procedural step improves reliability when testing whether $p_i\approx p_f$?

    Repeat trials and average results (report spread/uncertainty). Multiple trials reduce random errors and reveal consistency.

25. Which measurement tools are most appropriate to obtain cart velocities in a momentum lab?

    Photogates or motion sensor (or video analysis with scale). These tools measure velocity precisely without disturbing the motion.

26. Identify the best control to check for external impulse before running collisions.

    Verify constant velocity for a single cart: $\Delta v\approx 0$ over time. No velocity change confirms negligible external forces.

27. What conservation equation should you test for a two-cart interaction in 1D?

    $m_1v_{1i}+m_2v_{2i}=m_1v_{1f}+m_2v_{2f}$. Total momentum before equals total momentum after for two objects.

28. What formula should you use to compute the system momentum after collision in $1\text{D}$?

    $p_f=m_1v_{1f}+m_2v_{2f}$. Sum final momenta to compare with initial total momentum.

29. What calculation gives the percent difference used to judge momentum conservation?

    $\%\text{diff}=\frac{|p_f-p_i|}{|p_i|}\times 100\%$. Normalizes difference by initial value for comparison.

30. What graph would best show whether $p_f$ matches $p_i$ across many trials of different masses?

    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.

31. What condition must be met for a collision experiment to test momentum conservation in a system?

    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.

32. What is the dependent variable when testing whether total momentum is conserved?

    Difference between totals: $\Delta p=p_f-p_i$ (or percent difference). Measures how well momentum is conserved.

33. Which variable should you keep constant to isolate the effect of mass on momentum conservation results?

    Track conditions (levelness and friction) and the collision mechanism. Controls ensure only mass variation affects results.

34. Identify the missing step: you used photogates but did not know cart speed; what must be measured?

    Flag length $L$ to compute $v=\frac{L}{\Delta t}$. Photogate timing gives $\Delta t$; need $L$ for velocity.

35. Which option best reduces the effect of a small constant friction force during the collision interval?

    Use a short collision time and measure velocities immediately before and after. Minimizes impulse from friction during collision.

36. What condition must be met for momentum to be conserved in an experiment?

    Net external impulse is zero, $\sum J_{ext}=0$ (isolated system). No external forces means no external impulse to change total momentum.

37. What is the vector definition of linear momentum for an object used in conservation tests?

    $\vec{p}=m\vec{v}$. Momentum is mass times velocity, both magnitude and direction matter.

38. Which sign convention should you state when measuring 1D velocities for momentum calculations?

    Choose + direction along the track; opposite motion has negative $v$. Ensures consistent velocity signs for momentum calculations.

39. Compute $\%\text{diff}$ if $p_i=0.50$ and $p_f=0.47$ in $\text{kg}\cdot\text{m/s}$.

    $6\%$. $\%\text{diff}=\frac{|0.47-0.50|}{0.50}\times 100\%=6\%$

40. Which quantitative comparison best tests conservation: absolute difference or percent difference?

    Percent difference: $\frac{|p_f-p_i|}{\frac{|p_f|+|p_i|}{2}}\times 100\%$. Percent difference accounts for measurement scale and uncertainty.

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