Pattern 1: Work-Energy Theorem with Friction (Most Common)

Trigger words: "rough surface," "friction coefficient," "final speed"

Method:

1. Identify ALL forces acting (gravity, friction, applied, normal)
2. Calculate work done by each (W = Fd cos θ)
3. Apply W_net = $\Delta K$E

Key: Always check if the applied force has a vertical component — it changes the normal force and hence friction.

Pattern 2: Vertical Circular Motion

Trigger words: "vertical circle," "just completes," "minimum speed," "string breaks"

Method:

• Identify: string or rod?
• String: v_top(min) = √(gR); v_bottom(min) = √(5gR)
• Rod: v_top(min) = 0; v_bottom(min) = √(4gR)
• For tension: use centripetal force equation at that point

Classic trap: Applying string formula to rod. Options (a) = same for both = wrong.

Pattern 3: Elastic Collision (Equal Masses)

Trigger words: "elastic collision," "equal masses," "one at rest"

Result: Velocities exchange. Moving body stops; stationary body takes the initial velocity.

Pattern 4: Perfectly Inelastic Collision KE Loss

Trigger words: "perfectly inelastic," "stick together," "KE after collision"

Method: Find v_f from momentum conservation, then calculate KE_after = ½(m_{1}+m_{2})v_$f^{2}$. The trap: assuming KE = 0 after (wrong unless p_total = 0) or assuming KE is conserved (wrong).

Pattern 5: KE and Momentum Comparison

Trigger words: "equal KE," "equal momentum," "greater/less"

• Equal KE: heavier body has more momentum (p = √(2mKE) ∝ √m)
• Equal momentum: lighter body has more KE (KE = $p^{2}$/2m ∝ 1/m)