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
f₁ = 100 n f₂ = 100 n
← →
diagram 2
f₁ = 100 n
→
f₂ = 100 n
→
diagram 3
f₁ = 200 n f₂ = 100 n
← →
diagram 4
f₁ = 100 n f₂ = 200 n
← →
○ diagram 1
○ diagram 2
○ diagram 3
○ diagram 4

Explanation:

Step1: Recall Newton's Second Law

According to Newton's second law, the net force \( F_{net} = F_{left} - F_{right} \) (taking left as positive). The object accelerates left when \( F_{net}>0 \), i.e., \( F_{left}>F_{right} \).

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 left.

Step3: Analyze Diagram 2

Both \( F_1 \) and \( F_2 \) are rightward (\( 100\,\text{N each} \)).
\( F_{net} = 0 - (100 + 100) = -200\,\text{N} \) (negative means right). No acceleration left.

Step4: Analyze Diagram 3

\( F_1 = 200\,\text{N (left)} \), \( F_2 = 100\,\text{N (right)} \).
\( F_{net} = 200 - 100 = 100\,\text{N} \) (positive, so leftward acceleration).

Step5: Analyze Diagram 4

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

Answer:

Diagram 3