Question

conservation of momentum in an inelastic collision $m_1v_1 + m_2v_2 = (m_1 + m_2)v$ chapter review concept items 8.1 linear momentum, force, and impulse 1. what is impulse? a. change in velocity b. change in momentum c. rate of change of velocity d. rate of change of momentum 2. in which equation of newtons second law is mass assumed to be constant? a. $f = ma$ b. $f = \frac{delta p}{delta t}$ c. $f = delta pdelta t$ d. $f = \frac{delta m}{delta a}$

Explanation:

Step1: Recall the definition of impulse

Impulse \(J\) is defined as the change in momentum. Mathematically, \(J=\Delta p\) where \(\Delta p = p_{final}-p_{initial}\) and \(p = mv\) (momentum formula).

Step2: Analyze each option

• Option a: Change in velocity \(\Delta v\) is not impulse. Impulse is related to momentum change, not just velocity change.
• Option b: Since \(J=\Delta p\), this is correct.
• Option c: Rate of change of velocity \(\frac{\Delta v}{\Delta t}\) is acceleration \(a\), not impulse.
• Option d: Rate of change of momentum \(\frac{\Delta p}{\Delta t}\) is force \(F\) (from \(F=\frac{\Delta p}{\Delta t}\)), not impulse.

Step3: Recall Newton's second law forms

Newton's second law in the form \(F = ma\) (where \(a=\frac{\Delta v}{\Delta t}\) and \(p = mv\), so \(F=\frac{m\Delta v}{\Delta t}\) when \(m\) is constant) assumes mass \(m\) is constant.

• Option a: \(F = ma\) is the form where \(m\) is constant. We know \(a=\frac{\Delta v}{\Delta t}\) and \(F=\frac{\Delta(mv)}{\Delta t}\), when \(m\) is constant \(F = m\frac{\Delta v}{\Delta t}=ma\).
• Option b: \(F=\frac{\Delta p}{\Delta t}\) is the general form of Newton's second law (works even when \(m\) is not constant, as \(p = mv\) and if \(m\) changes \(F=\frac{v\Delta m + m\Delta v}{\Delta t}\)).
• Option c: \(F=\Delta p\Delta t\) is not a correct form of Newton's second law.
• Option d: \(F=\frac{\Delta m}{\Delta a}\) is not a valid form of Newton's second law.

Answer:

1. B. Change in momentum
2. A. \(F = ma\)