Question

1. if four objects (a, b, c, and d) each experience a constant force and have accelerations of 2 m/s², 4 m/s², 1 m/s², and 3 m/s², rank them from greatest to least mass.

Explanation:

Step1: Recall Newton's Second Law

Newton's second law is given by \( F = ma \), where \( F \) is force, \( m \) is mass, and \( a \) is acceleration. Rearranging for mass, we get \( m=\frac{F}{a} \). Since the force \( F \) is constant for all objects, mass \( m \) is inversely proportional to acceleration \( a \) (i.e., \( m\propto\frac{1}{a} \)).

Step2: Analyze the accelerations

The accelerations of the objects are: \( a_A = 2\space m/s^2 \), \( a_B = 4\space m/s^2 \), \( a_C = 1\space m/s^2 \), \( a_D = 3\space m/s^2 \).

Step3: Rank the masses based on inverse proportionality

Since \( m\propto\frac{1}{a} \), the smaller the acceleration, the larger the mass.

• For \( a_C = 1\space m/s^2 \) (smallest acceleration), mass \( m_C \) is largest.
• Next, \( a_A = 2\space m/s^2 \), so \( m_A \) is next.
• Then, \( a_D = 3\space m/s^2 \), so \( m_D \) is next.
• Finally, \( a_B = 4\space m/s^2 \) (largest acceleration), so \( m_B \) is smallest.

So the ranking from greatest to least mass is \( C, A, D, B \).

Answer:

\( C, A, D, B \)