Question

in an investigation over force, mass, and acceleration, five different students lined up behind five different objects. each student pushed their assigned object with the same amount of force as the other students. the distance traveled by each object is listed in the table. based on the data displayed in the table, which of the following conclusions can be made concerning the objects involved in the investigation? select two correct answers. object 3 had the greatest mass. all of the objects were made of different material. objects 1, 3, and 5 were made of different material than objects 2 and 4. object 4 had the greatest mass. object 4 had the least mass.

Explanation:

Step1: Recall Newton's second - law

According to Newton's second - law $F = ma$ (where $F$ is force, $m$ is mass, and $a$ is acceleration). When the force $F$ is constant, the acceleration $a$ is inversely proportional to the mass $m$ ($a=\frac{F}{m}$). Also, from the kinematic equation $d = v_0t+\frac{1}{2}at^{2}$, assuming the objects start from rest ($v_0 = 0$), $d=\frac{1}{2}at^{2}$. When the time of pushing is the same for all objects, the distance $d$ is proportional to the acceleration $a$. So, the object that travels the greatest distance has the greatest acceleration and the least mass, and the object that travels the least distance has the least acceleration and the greatest mass.

Step2: Analyze the distances

Object 3 traveled 3 meters (the least distance among the objects), so it has the least acceleration and thus the greatest mass. Object 4 traveled 15 meters (the greatest distance among the objects), so it has the greatest acceleration and the least mass.

Answer:

Object 3 had the greatest mass.
Object 4 had the least mass.