Question

The chart lists the masses and velocities of four objects.

A 3-column table with 4 rows titled Motion of 4 Objects. The first column labeled Object has entries W, X, Y, Z. The second column labeled Mass (kilograms) has entries 58, 34, 89, 60. The third column labeled Velocity (meters per second) has entries 1, 2, 0.5, 2.
Which object requires the greatest change in momentum in order to stop its motion?

W
X
Y
Z

Answer 1

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:

1. **Object W**
- Mass: 58 kg
- Velocity: 1 m/s
- Momentum: \( p_W = 58 \, \text{kg} \times 1 \, \text{m/s} = 58 \, \text{kg} \cdot \text{m/s} \)

2. **Object X**
- Mass: 34 kg
- Velocity: 2 m/s
- Momentum: \( p_X = 34 \, \text{kg} \times 2 \, \text{m/s} = 68 \, \text{kg} \cdot \text{m/s} \)

3. **Object Y**
- Mass: 89 kg
- Velocity: 0.5 m/s
- Momentum: \( p_Y = 89 \, \text{kg} \times 0.5 \, \text{m/s} = 44.5 \, \text{kg} \cdot \text{m/s} \)

4. **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.