Questions: Object A has a mass m and a speed v, object B has a mass m / 2 and a speed 4 v, and object C has a mass 3 m and a speed v / 3. Rank the objects according to the magnitude of their momentum. Rank from smallest to largest. To rank items as equivalent, overlap them. Object C Object A Object B Smallest momentum Largest momentum

Solution Steps

The momentum \( p \) of an object is given by the formula: \[ p = mv \] where \( m \) is the mass and \( v \) is the velocity of the object.

Let's calculate the momentum for each object:

• Object A: \[ p_A = m \cdot v \]

• Object B: \[ p_B = \frac{m}{2} \cdot 4v = 2mv \]

• Object C: \[ p_C = 3m \cdot \frac{v}{3} = mv \]

Now, we compare the magnitudes of the momenta:

• \( p_A = mv \)
• \( p_B = 2mv \)
• \( p_C = mv \)

From the calculated momenta, we can rank the objects as follows:

• Object A and Object C have the same momentum: \( mv \)
• Object B has the largest momentum: \( 2mv \)

Thus, the ranking from smallest to largest momentum is: \[ \text{Object A} = \text{Object C} < \text{Object B} \]

Final Answer