Angled Applied Force and Minimum Force
At impending horizontal motion under an upward pull, F cos alpha=mu_s(mg-F sin alpha); tan alpha_opt=mu_s.
Why this shows up in the exam
Pull versus push · Minimum force · Wall adhesion
Learn the idea
An angled force changes both drive and normal reaction, hence friction. Pulling upward lightens contact; pushing downward increases it.
🧠 Memory hook: An upward pull drives and lightens.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- F cos(alpha)=mu_s(mg-F sin(alpha)) — threshold pull
- tan(alpha_opt)=mu_s — minimum-force angle
- F_min=mu_s m g/sqrt(1+mu_s²) — minimum pull
How to approach it
- 1Resolve F
- 2Recompute N
- 3Solve threshold then optimize
Common slip-ups that cost marks
- •Keeping N=mg
- •Using pull signs for push
- •Optimizing too early
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A 2 kg block moves on a horizontal rough surface with coefficient of kinetic friction 0.2. A horizontal force of 10 N acts on it. Take g = 10 m/s^2. What is its acceleration?
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