Successive Collisions with a Surface (Edexcel A-Level Further Mathematics): Quizzes

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Successive Collisions with a Surface
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What happens to the parallel component of velocity when a sphere collides with a smooth plane?

It remains unchanged

What is the formula for perpendicular velocity after collision in terms of ee and v⊥v_{\perp}?

v⊥,after=−ev⊥,beforev_{\perp, \text{after}} = -e v_{\perp, \text{before}}

What is the valid range for the coefficient of restitution ee?

0≤e≤10 \leq e \leq 1

What is the rebound height after the nnth collision with initial height h0h_0?

hn=e2nh0h_n = e^{2n} h_0

What is the perpendicular velocity after nn collisions with initial v⊥,0v_{\perp, 0}?

v⊥,n=(−e)nv⊥,0v_{\perp, n} = (-e)^n v_{\perp, 0}

A sphere hits a surface at 8 ms−18 \, \text{ms}^{-1}. If e=0.5e = 0.5, what is the rebound speed?

4 ms−14 \, \text{ms}^{-1}

If first rebound height is 1 m1 \, \text{m} and e=0.8e = 0.8, what is the second rebound height?

0.64 m0.64 \, \text{m}

A sphere hits a vertical wall with u=(5−3)\mathbf{u} = \begin{pmatrix} 5 \\ -3 \end{pmatrix}. What is u⊥\mathbf{u}_{\perp}?

(50)\begin{pmatrix} 5 \\ 0 \end{pmatrix}

What happens to kinetic energy during a collision with e<1e < 1?

Some kinetic energy is lost

What formula gives speed just before impact for a sphere dropped from height hh?

v=2ghv = \sqrt{2gh}

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