Question

1. if two balls have the same mass but different velocities, which one has more momentum? why?

Explanation:

Step1: Recall the momentum formula

The formula for momentum \( p \) is given by \( p = mv \), where \( m \) is the mass of the object and \( v \) is its velocity.

Step2: Analyze the given condition

We know that the two balls have the same mass, i.e., \( m_1 = m_2 = m \), but different velocities, let's say \( v_1 \) and \( v_2 \) where \( v_1
eq v_2 \).

Step3: Compare the momenta

Using the momentum formula, the momentum of the first ball \( p_1 = m v_1 \) and the momentum of the second ball \( p_2 = m v_2 \). Since \( m \) is constant (same for both), the momentum is directly proportional to the velocity. So, if \( v_1>v_2 \), then \( p_1 = m v_1>m v_2 = p_2 \), and if \( v_2 > v_1 \), then \( p_2=m v_2>m v_1 = p_1 \).

Answer:

The ball with the greater velocity has more momentum. This is because momentum \( p \) is given by the formula \( p = mv \) (where \( m \) is mass and \( v \) is velocity). When the mass \( m \) is constant, momentum is directly proportional to velocity, so a higher velocity results in a higher momentum.