Question

an engineer applies the same amount of force to two different objects. object a accelerates three times as much as object b. what can you conclude about their masses? object a has three times the mass of object b object b has three times the mass of object a. they have the same mass object a has no mass

Explanation:

Step1: Use Newton's second law

Newton's second law is \(F = ma\), where \(F\) is force, \(m\) is mass, and \(a\) is acceleration. Let the force on both objects be \(F\). For object \(A\), \(F=m_Aa_A\). For object \(B\), \(F = m_Ba_B\). Since \(F\) is the same for both, \(m_Aa_A=m_Ba_B\).

Step2: Substitute the relationship between accelerations

We know that \(a_A = 3a_B\). Substitute \(a_A\) into \(m_Aa_A=m_Ba_B\). So \(m_A\times3a_B=m_Ba_B\).

Step3: Solve for the ratio of masses

Divide both sides of the equation \(m_A\times3a_B=m_Ba_B\) by \(a_B\) (since \(a_B
eq0\)). We get \(3m_A=m_B\), which means \(m_B = 3m_A\).

Answer:

Object B has three times the mass of Object A.