Free body diagram — how to draw FBD for any mechanics problem

Question

A 5 kg block is placed on a rough inclined plane (angle $30°$ , coefficient of friction $\mu = 0.3$ ). Draw the free body diagram and find whether the block slides or stays.

(CBSE 11 + JEE Main + NEET)

Solution — Step by Step

Remove everything except the block. Now list every force acting ON the block:

Weight $mg = 5 \times 10 = 50$ N (vertically downward)
Normal force $N$ (perpendicular to the incline surface)
Friction $f$ (along the incline, opposing tendency of motion)

That is it. No other force acts on the block. Do NOT include the force the block exerts on the surface — that acts on the surface, not on the block.

Resolve $mg$ into components:

Along the incline (downward): $mg\sin 30° = 50 \times 0.5 = 25$ N
Perpendicular to incline: $mg\cos 30° = 50 \times 0.866 = 43.3$ N

No acceleration perpendicular to the surface:

N = mg\cos 30° = 43.3 \text{ N}

Maximum static friction: $f_{max} = \mu N = 0.3 \times 43.3 = 13$ N

Force pulling the block down the incline: $mg\sin 30° = 25$ N

Maximum friction resisting: $f_{max} = 13$ N

Since $25 > 13$ , friction cannot hold the block. The block slides down.

Net force = $25 - 13 = 12$ N, acceleration $= 12/5 = \mathbf{2.4 \text{ m/s}^2}$ down the incline.

flowchart TD
    A["FBD Drawing Algorithm"] --> B["Step 1: Isolate the body"]
    B --> C["Step 2: Draw weight mg downward"]
    C --> D["Step 3: Draw Normal N perpendicular to contact surface"]
    D --> E["Step 4: Draw friction along surface opposing motion"]
    E --> F{"Any other forces? Tension, applied, spring?"}
    F -- Yes --> G["Add them with correct direction"]
    F -- No --> H["Step 5: Choose axes, resolve forces"]
    G --> H
    H --> I["Step 6: Apply F = ma along each axis"]
    I --> J["Solve for unknowns"]

Why This Works

Newton’s second law ( $\vec{F}_{net} = m\vec{a}$ ) applies to a single body. The FBD shows ALL forces on that body and nothing else. By isolating the body, we ensure we count every force exactly once and do not accidentally include reaction forces that act on other objects.

Choosing axes along and perpendicular to the incline simplifies the math because acceleration (if any) is along the incline. This makes one component of acceleration zero, giving us the normal force directly.

Alternative Method

Instead of resolving $mg$ , you can use the condition for sliding directly:

The block slides if $\tan\theta > \mu$ , i.e., $\tan 30° > 0.3$ .

$\tan 30° = 0.577 > 0.3$ . So the block slides.

This shortcut avoids resolving forces altogether — useful for MCQs.

The angle at which a block JUST starts to slide on a rough incline is called the angle of repose: $\theta_r = \tan^{-1}(\mu)$ . If the incline angle exceeds $\theta_r$ , the block slides. This single formula replaces the entire FBD calculation for “will it slide?” questions.

Common Mistake

The most common FBD error: including forces that do not act on the body. The block pushes on the surface (Newton’s third law), but that force acts on the SURFACE, not on the block. Only draw forces that act ON the object in your FBD. Another frequent error: drawing friction in the wrong direction. Friction always opposes the tendency of motion — if the block tends to slide down, friction acts up the incline.

Question

Solution — Step by Step

Why This Works

Alternative Method

Common Mistake

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