Math Problem Statement
Solution
Let’s analyze and solve the questions presented:
Question A: Initial Momentum of the Carts Before Collision
- **Given dataLet’s analyze and solve the questions presented:
Question A: Initial Momentum of the Carts Before Collision
-
**Given **
- Mass of Cart A = Mass of Cart B = 98 kg
- Velocity of Cart A () = 3.0 m/s (moving to the right)
- Velocity of Cart B () = -1.5 m/s (moving to the left)
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Calculate Initial Momentum of Each Cart:
- Momentum of Cart A () =
- Momentum of Cart B () =
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Total Initial Momentum:
- Total momentum =
So, the correct answer for the initial momentum is 147 kg m/s.
Question B: Maximum Velocity of Cart A After Collision
Given that Cart B moves backward at 0.75 m/s after the collision, we want to find the maximum velocity of Cart A.
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Using Conservation of Momentum:
- The total momentum before the collision is 147 kg m/s, and this must be conserved.
- Let the velocity of Cart A after the collision be .
- Momentum of Cart B after collision () = .
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Calculate :
- Total momentum after collision = Momentum of Cart A + Momentum of Cart B
- Solving for :
Therefore, the maximum velocity of Cart A after the collision is 2.25 m/s.
Would you like further details on these calculations or have any other questions?
Further Questions to Consider
- How would the initial momentum change if Cart B had a different mass?
- What would happen if this collision were inelastic rather than elastic?
- How does conservation of momentum apply in different types of collisions?
- How would you calculate the kinetic energy of each cart before and after the collision?
- Can we determine the energy lost or gained in this collision?
Tip
In elastic collisions, both momentum and kinetic energy are conserved. This can simplify solving for final velocities.
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Math Problem Analysis
Mathematical Concepts
Physics
Momentum Conservation
Elastic Collisions
Formulas
Momentum formula: p = m * v
Total momentum conservation: p_initial = p_final
Theorems
Conservation of Momentum
Suitable Grade Level
Grades 9-12
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