Solve for mass using a graph of a collision

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SUMMARY

The discussion focuses on calculating the mass of cart A using the principles of momentum conservation during a collision. The user applied the equation m_{s} Δv_{s} = -m_{A} Δv_{A} with values derived from a velocity-time graph. The calculated change in velocity for cart A (ΔvA) was approximately -2 m/s, and for the standard cart (Δvs), it was about 4.25 m/s. The resulting mass of cart A was computed to be 2.13 kg, which the user later identified as incorrect, indicating a need for further assistance in the calculations.

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  • Understanding of momentum conservation principles
  • Ability to interpret velocity-time graphs
  • Familiarity with basic algebra for solving equations
  • Knowledge of units of mass and velocity
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  • Review the concept of momentum conservation in collisions
  • Learn how to accurately extract data from velocity-time graphs
  • Practice solving similar problems involving collisions and mass calculations
  • Explore the effects of friction on momentum in collisions
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Students studying physics, particularly those focusing on mechanics and collision problems, as well as educators looking for examples of momentum conservation applications.

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Homework Statement


A 1-kg standard cart collides with a cart A of unknown inertia. Both carts appear to be rolling with significant wheel friction because their velocities change with time as shown in. What is the mass of cart A?

The graph below should be used to solve for the mass.
sPtKc3c.png




Homework Equations


[itex]m_{s} \Delta v_{s} = -m_{A} \Delta v_{A}[/itex]


The Attempt at a Solution



I calculated ΔvA using the graph, to be ~-2 m/s, because the velocity before the collision is ~4 m/s and afterwards it is ~2 m/s, so 2(m/s) - 4(m/s) = -2 m/s, simple. I calculated Δvs to be ~4.25 m/s because the velocity changes from 0 m/s to 4.25 m/s. So the equation becomes 1 (kg) * 4.25 (m/s) = - mA (kg) * (-2 m/s). Which when I multiplied out, and solved for mA. I got 2.13 kg. Which, apparently, is wrong. Please help!
 
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