Question

1. choose the best response:

• claim: gravitational acceleration is ______ (directly proportional to, inversely proportional to, or independent of) mass.
• evidence: the graph of gravitational acceleration vs. mass is ______ (an increasing line, a decreasing line, a horizontal line).
• reasoning: this shows that as mass increases, gravitational acceleration ______ (increases, decreases, remains the same).

1. based on our graph, what is the approximate gravitational acceleration of all objects in free fall on earth?

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1. if an objects mass is 0.1 kg, what is its gravitational acceleration on earth?

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1. if an objects mass is 5 kg, what is its gravitational acceleration on earth?

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1. if an objects mass is 1,000 kg, what is its gravitational acceleration on earth?

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Explanation:

Question 8

Step1: Recall Gravitational Acceleration Concept

Gravitational acceleration \( g \) near Earth's surface is given by \( g=\frac{GM}{r^{2}} \), where \( G \) is gravitational constant, \( M \) is Earth's mass, \( r \) is Earth's radius. It does not depend on the mass of the object (\( m \)). So gravitational acceleration is independent of mass.

Step2: Analyze Graph of \( g \) vs. \( m \)

Since \( g \) is independent of \( m \), as \( m \) changes, \( g \) remains constant. So the graph of \( g \) vs. \( m \) is a horizontal line (constant value).

Step3: Deduce Relationship from Graph

A horizontal line means that as mass (\( m \)) increases, gravitational acceleration (\( g \)) remains the same (since the \( y \)-value ( \( g \)) does not change with \( x \)-value ( \( m \))).

Step1: Recall Earth's Gravitational Acceleration

From physics, the approximate gravitational acceleration of objects in free fall on Earth is \( 9.8\ m/s^{2} \) (or sometimes approximated as \( 10\ m/s^{2} \) for simplicity, but \( 9.8\ m/s^{2} \) is the standard approximate value).

Step1: Recall Independence of \( g \) from Mass

Gravitational acceleration \( g \) near Earth's surface is independent of the mass of the object. So regardless of the mass (0.1 kg here), \( g \) is approximately \( 9.8\ m/s^{2} \).

Answer:

• Claim: independent of
• Evidence: a horizontal line
• Reasoning: remains the same

Question 9