# Newton’s Law of Restitution

While having numerous similarities with STPM Physics Syllables, the mechanics section in A-Level Further Mathematics has different emphasis, and some equations that is not taught in STPM.

So far these are some of the new equations that I have discovered during my practice:

1) Newton’s Law of Restitution (Taught in STPM, but less emphasized)

2) Perpendicular Axis Theorem and Parallel Axis Theorem

3) Center of Mass for Certain Geometry Shape

I will disuss the Coefficient of Restitution today.

The **Coefficient of Restitution, **is the ratio of relative velocity of separation to relative velocity of approach. In equation form,

v2 – v1 = e (u1 – u2)

where e is the coefficient of restitution. e has a value between 0 and 1, 1 being the case for no kinetic energy is lost. The lower the coefficient, the more is the lost of kinetic energy from the system.

Sample Question :

A table tennis ball of mass 2.5 g strikes the smooth surface of a horizontal table. Calculate:

1) The speed of the ball immediately after impact, [2]

2) The coefficient of restitution between the ball and the table. [2]

(*Adapted from A-Level Further Maths*, *Specimen Paper 1)*

Hints :

1) The** vertical component **of linear momentum is not conserved here, since the tennis ball will experience an impulsive force upon hitting the surface. Only the **horizontal component** is conserved.

2) In this case, u2 and v2 = 0, since the wall is not moving. Con sider only the **vertical component **of velocity.

um, hope u won’t consider it audacious of me to ask, but…could you give me a few examples of impressive math calculations (as in kinematic, but if possible simpler) dat can be understood at SPM, or if possible, PMR level? i hope it’s not too much to ask…n please don’t tell me my comment is caught in spam again.

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