Question

1. based on newtons second law ($f = ma$), what do you predict would happen to your acceleration values if your balloon rocket had twice the mass? ______ half the mass? ______.

Explanation:

Step1: Analyze when mass is twice

According to \(F = ma\), when \(F\) is constant (assuming the force from the balloon rocket remains the same), if \(m\) becomes \(2m\), then \(a=\frac{F}{m}\) becomes \(a'=\frac{F}{2m}\). So the acceleration is halved.

Step2: Analyze when mass is half

When \(F\) is constant and \(m\) becomes \(\frac{m}{2}\), then \(a''=\frac{F}{\frac{m}{2}} = 2\frac{F}{m}\). So the acceleration is doubled.

Answer:

If the balloon rocket had twice the mass, the acceleration values would be halved. If the balloon rocket had half the mass, the acceleration values would be doubled.