Question

multiple select question
select all that apply
which statements correctly describe a system of two people on in-line skates, initially at rest until one person pushes against the other?

the total momentum after the push is zero.
the total momentum after the push will be greater than zero.
the total momentum after the push will be less than zero.
the total momentum before the push is zero.

Explanation:

1. Momentum before push: The system (two people) is initially at rest, so velocity \( v = 0 \). Momentum \( p = mv \), so total momentum \( p_{\text{total, before}} = m_1v_1 + m_2v_2 = 0 + 0 = 0 \). Thus, "The total momentum before the push is zero" is correct.
2. Momentum after push: By the law of conservation of momentum, the total momentum of an isolated system (no external forces here, as the push is internal) remains constant. Since initial total momentum is zero, final total momentum \( p_{\text{total, after}} = p_{\text{total, before}} = 0 \). So "The total momentum after the push is zero" is correct. The other two options (greater than zero, less than zero) contradict conservation of momentum.

Answer:

A. The total momentum after the push is zero.
D. The total momentum before the push is zero.