Solving a Problem: What Went Wrong & Velocity for Both Masses

  • Thread starter Mohmmad Maaitah
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In summary, the examiner provided a solution that switched the masses, but your work was correct. You also asked if the velocity is the same for both masses, and the answer is yes since they are connected. However, they move in different directions.
  • #1
Mohmmad Maaitah
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Homework Statement
As in the first provided picture:
Relevant Equations
Newton second law
This is the problem:
1683368077531.png


And this the answer provided by the examiner:
1683367960587.png

And this is my own answer:
IMG_20230506_130351_883.jpg


So what did I get wrong???
Also I want to know if the Velocity is the same for both masses.
 

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  • #2
Mohmmad Maaitah said:
So what did I get wrong???
The diagram shows m_1 as the hanging mass, but the given solution switches that. Your work is fine.
Mohmmad Maaitah said:
Also I want to know if the Velocity is the same for both masses.
Sure---they are connected. (The speeds are the same, but they move in different directions, of course.)
 
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  • #3
Doc Al said:
The diagram shows m_1 as the hanging mass, but the given solution switches that. Your work is fine.

Sure---they are connected. (The speeds are the same, but they move in different directions, of course.)
Oh lord, he switched the masses :doh:
 

FAQ: Solving a Problem: What Went Wrong & Velocity for Both Masses

What are the common reasons for errors in solving problems involving velocity for two masses?

Common reasons for errors include incorrect application of conservation laws (like momentum and energy), miscalculations in algebra, not accounting for all forces acting on the masses, incorrect initial conditions, and neglecting friction or air resistance if they are relevant to the problem.

How do you apply the conservation of momentum to solve for the velocities of two masses after a collision?

To apply the conservation of momentum, you set the total momentum before the collision equal to the total momentum after the collision. This can be expressed as \( m_1 v_{1i} + m_2 v_{2i} = m_1 v_{1f} + m_2 v_{2f} \), where \( m_1 \) and \( m_2 \) are the masses, and \( v_{1i} \), \( v_{2i} \), \( v_{1f} \), and \( v_{2f} \) are the initial and final velocities of the masses, respectively.

What role does the type of collision (elastic or inelastic) play in determining the final velocities of the masses?

In an elastic collision, both momentum and kinetic energy are conserved. This gives two equations to solve for the final velocities. In an inelastic collision, only momentum is conserved, and the kinetic energy is not, which typically results in the masses sticking together and moving with a common velocity after the collision.

How do you solve for the final velocities if the collision is perfectly inelastic?

In a perfectly inelastic collision, the two masses stick together after the collision. You can use the conservation of momentum to find the common final velocity: \( (m_1 + m_2)v_f = m_1 v_{1i} + m_2 v_{2i} \). Solving for \( v_f \) gives \( v_f = \frac{m_1 v_{1i} + m_2 v_{2i}}{m_1 + m_2} \).

What are the key steps to check if your solution for the velocities is correct?

Key steps include verifying that the conservation of momentum equation is satisfied, checking if the kinetic energy is conserved in the case of an elastic collision, ensuring that all forces and initial conditions are correctly accounted for, and rechecking the algebraic calculations for any errors. Additionally, consider the physical reasonableness of the final velocities.

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