Question

practice it!
pablo and prieta are investigating force and motion. they have two boxes of the same size filled with different materials. they apply the same amount of force to each box and record the distance traveled. they recorded their measurements in a data table.
select the statement(s) that are accurate conclusions based on the data table.
the amount of force applied had less effect on the box with more mass.
the box with more mass traveled less distance than the box with less mass.
the amount of force applied had more effect on the box with less mass.
the relationship between mass and force cannot be determined with the current data.
the box with less mass traveled further than the box with more mass.

Explanation:

Step1: Analyze the relationship between force, mass and motion

According to Newton's second law \(F = ma\) (where \(F\) is force, \(m\) is mass and \(a\) is acceleration), and the kinematic equation \(s=v_0t+\frac{1}{2}at^{2}\) (assuming \(v_0 = 0\), \(s=\frac{1}{2}at^{2}\)). When force \(F\) is constant, \(a=\frac{F}{m}\), so \(s=\frac{F}{2m}t^{2}\).

Step2: Evaluate each statement

• Statement 1: The box with less mass traveled further than the box with more mass.

Since \(s=\frac{F}{2m}t^{2}\) ( \(F\) and \(t\) are constant in this experiment), when \(m\) is smaller, \(s\) is larger. So this statement is correct.

• Statement 2: The relationship between mass and force cannot be determined with the current data.

The experiment is about force and motion (with mass as a variable affecting motion), not directly about the relationship between mass and force. The data is about how force (constant) affects the motion (distance traveled) of objects with different masses. So this statement is correct.

• Statement 3: The amount of force applied had more effect on the box with less mass.

From \(a=\frac{F}{m}\), for a given \(F\), smaller \(m\) gives larger \(a\), and from \(s=\frac{1}{2}at^{2}\), larger \(a\) (with same \(t\)) gives larger \(s\). So the force has a more “visible” (in terms of distance traveled) effect on the box with less mass. This statement is correct.

• Statement 4: The box with more mass traveled less distance than the box with less mass.

As \(s=\frac{F}{2m}t^{2}\) ( \(F\) and \(t\) constant), larger \(m\) means smaller \(s\). So this statement is correct.

• Statement 5: The amount of force applied had less effect on the box with more mass.

Since \(a = \frac{F}{m}\), larger \(m\) gives smaller \(a\), and from \(s=\frac{1}{2}at^{2}\), smaller \(a\) (with same \(t\)) gives smaller \(s\). So the force has a less “visible” (in terms of distance traveled) effect on the box with more mass. This statement is correct.

Answer:

All statements (The box with less mass traveled further than the box with more mass; The relationship between mass and force cannot be determined with the current data; The amount of force applied had more effect on the box with less mass; The box with more mass traveled less distance than the box with less mass; The amount of force applied had less effect on the box with more mass) are correct.