Question

fill in the blank question
the graph shows how the acceleration of a rocket depends on different payloads it is carrying. the force of the rocket is the same in both cases. according to what newtons second law of motion says about the relationship between acceleration, force, and mass, payload has a higher mass.

Explanation:

Step1: Recall Newton's second law

Newton's second law is \(F = ma\), where \(F\) is force, \(m\) is mass, and \(a\) is acceleration. We can rewrite it as \(m=\frac{F}{a}\). Since \(F\) is constant (given), mass \(m\) is inversely proportional to acceleration \(a\).

Step2: Analyze the graph for acceleration

The steeper the speed - time graph, the greater the acceleration (\(a=\frac{\Delta v}{\Delta t}\)). Payload A has a steeper graph, so \(a_A > a_B\).

Step3: Determine the mass using the inverse - proportion

Since \(m=\frac{F}{a}\) and \(F\) is constant, when \(a\) is smaller, \(m\) is larger. Because \(a_A > a_B\), then \(m_B>m_A\)

Answer:

Payload B