Elastic Collisions in 1D (Edexcel A-Level Further Mathematics): Quizzes

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Energy in 1D and Successive Collisions
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What does Newton's law of restitution define the coefficient of restitution (ee) as?

speed of separationspeed of approach\frac{\text{speed of separation}}{\text{speed of approach}}

What is the conservation of momentum equation for two colliding spheres?

mAuA+mBuB=mAvA+mBvBm_A u_A + m_B u_B = m_A v_A + m_B v_B

When do further impacts occur between two spheres after a collision?

When vB>vAv_B > v_A

For a sphere colliding with a smooth plane, how is ee calculated?

e=vreboundvimpacte = \frac{v_{\text{rebound}}}{v_{\text{impact}}}

In Example 1, sphere A (2 kg at 4 ms⁻¹) hits sphere B (3 kg at 1 ms⁻¹, e=0.8e=0.8). What is vAv_A?

0.76 ms⁻¹

In Example 1, will spheres A and B collide again after their first collision?

Yes, they will collide again

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

v=2ghv = \sqrt{2gh}

What formula gives the rebound height after a sphere bounces with velocity vv?

h=v22gh = \frac{v^2}{2g}

When e<1e < 1, what happens to kinetic energy during collisions?

Kinetic energy is not conserved

What happens to successive rebounds when e<1e < 1 for a sphere bouncing on a plane?

Rebounds decrease in height

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