Question

the free body diagrams below show four ways that two different forces could be exerted on an object.

in which diagram will the object accelerate toward the left?

diagram 1
$f_1 = 100\\ n$ $f_2 = 100\\ n$
$xleftarrow{}$ $xrightarrow{}$

diagram 2
$f_1 = 100\\ n$
$xleftarrow{}$ $xrightarrow{}$
$f_2 = 100\\ n$
$xleftarrow{}$ $xrightarrow{}$

diagram 3
$f_1 = 200\\ n$ $f_2 = 100\\ n$
$xleftarrow{}$ $xrightarrow{}$

diagram 4
$f_1 = 100\\ n$ $f_2 = 200\\ n$
$xleftarrow{}$ $xrightarrow{}$

\bigcirc diagram 1

\bigcirc diagram 2

\bigcirc diagram 3

\bigcirc diagram 4

Explanation:

Step1: Recall Newton's Second Law

Acceleration direction depends on net force. Net force \( F_{net} = F_{left} - F_{right} \) (left forces positive, right negative).

Step2: Analyze Diagram 1

\( F_1 = 100\,\text{N (left)}, F_2 = 100\,\text{N (right)} \). \( F_{net} = 100 - 100 = 0\,\text{N} \). No acceleration.

Step3: Analyze Diagram 2

Both \( F_1, F_2 = 100\,\text{N (right)} \). Net force right, acceleration right.

Step4: Analyze Diagram 3

\( F_1 = 200\,\text{N (left)}, F_2 = 100\,\text{N (right)} \). \( F_{net} = 200 - 100 = 100\,\text{N (left)} \). Acceleration left.

Step5: Analyze Diagram 4

\( F_1 = 100\,\text{N (left)}, F_2 = 200\,\text{N (right)} \). \( F_{net} = 100 - 200 = -100\,\text{N (right)} \). Acceleration right.

Answer:

Diagram 3