Question

1. if four objects (a, b, c, and d) are pushed with equal force, and their masses are in the order of 5 kg, 2 kg, 7 kg, and 3 kg, rank them from greatest to least acceleration.

Explanation:

Step1: Recall Newton's Second Law

Newton's second law states \( F = ma \), where \( F \) is force, \( m \) is mass, and \( a \) is acceleration. Rearranging for acceleration, we get \( a=\frac{F}{m} \).

Step2: Analyze the Relationship

Since the force \( F \) is equal for all objects, acceleration \( a \) is inversely proportional to mass \( m \) (i.e., \( a\propto\frac{1}{m} \)). So, the smaller the mass, the greater the acceleration.

Step3: List the Masses

• Object A: \( 5\space kg \)
• Object B: \( 2\space kg \)
• Object C: \( 7\space kg \)
• Object D: \( 3\space kg \)

Step4: Rank by Acceleration

From the inverse relationship, we rank the masses from smallest to largest (since smaller mass means greater acceleration): \( 2\space kg \) (B) \( < 3\space kg \) (D) \( < 5\space kg \) (A) \( < 7\space kg \) (C). Thus, the acceleration ranking from greatest to least is \( B > D > A > C \).

Answer:

\( B > D > A > C \)