To determine which object requires the greatest change in momentum to stop its motion, we first need to calculate the momentum of each object. The momentum \( p \) of an object is given by the formula:
\[ p = m \cdot v \]
where \( m \) is the mass and \( v \) is the velocity.
Using the data provided in the table:
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Object W
- Mass: 58 kg
- Velocity: 1 m/s
- Momentum: \( p_W = 58 , \text{kg} \times 1 , \text{m/s} = 58 , \text{kg} \cdot \text{m/s} \)
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Object X
- Mass: 34 kg
- Velocity: 2 m/s
- Momentum: \( p_X = 34 , \text{kg} \times 2 , \text{m/s} = 68 , \text{kg} \cdot \text{m/s} \)
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Object Y
- Mass: 89 kg
- Velocity: 0.5 m/s
- Momentum: \( p_Y = 89 , \text{kg} \times 0.5 , \text{m/s} = 44.5 , \text{kg} \cdot \text{m/s} \)
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Object Z
- Mass: 60 kg
- Velocity: 2 m/s
- Momentum: \( p_Z = 60 , \text{kg} \times 2 , \text{m/s} = 120 , \text{kg} \cdot \text{m/s} \)
Now we have the momenta for each object:
- Object W: 58 kg·m/s
- Object X: 68 kg·m/s
- Object Y: 44.5 kg·m/s
- Object Z: 120 kg·m/s
Since stopping an object requires a change in momentum equal to its current momentum, the object that requires the greatest change in momentum to stop its motion is the one with the highest momentum.
Answer: Object Z (120 kg·m/s) requires the greatest change in momentum to stop.
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