A $1 ext{ kg}$ object strikes a wall with velocity $1 ext{ ms}^{-1}$ at an angle of $60^\circ$ with the wa

Question

A $1 	ext{ kg}$ object strikes a wall with velocity $1 	ext{ ms}^{-1}$ at an angle of $60^\circ$ with the wall and reflects at the same angle. If it remains in contact with the wall for $0.1 	ext{ s}$, then the force exerted on the wall is:

Accepted Answer

1. **Identify Given Data:** 
   - Mass $m = 1 	ext{ kg}$ (inferred from input artifact '111').
   - Velocity $v = 1 	ext{ m/s}$ (inferred from input artifact '111').
   - Angle with wall $	heta = 60^\circ$.
   - Time of contact $\Delta t = 0.1 	ext{ s}$.
2. **Analyze Momentum Change:** 
   - The component of velocity parallel to the wall ($v \cos 60^\circ$) remains unchanged.
   - The component of velocity perpendicular to the wall ($v \sin 60^\circ$) reverses direction.
   - Initial perpendicular momentum $p_i = m v \sin 60^\circ$.
   - Final perpendicular momentum $p_f = -m v \sin 60^\circ$ (taking opposite direction).
   - Change in momentum $|\Delta p| = |p_f - p_i| = 2mv \sin 60^\circ$ [Source 133].
3. **Calculate Impulse:**
   $$ \Delta p = 2 	imes 1 	imes 1 	imes \frac{\sqrt{3}}{2} = \sqrt{3} 	ext{ kg m/s} $$
4. **Calculate Force:**
   - Average force $F = \frac{\Delta p}{\Delta t}$.
   $$ F = \frac{\sqrt{3}}{0.1} = 10\sqrt{3} 	ext{ N} $$
   [Source 132, 144]

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