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Newton’s Law of Restitution

January 9, 2008

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.



2 Comments leave one →
  1. nightstar permalink
    January 13, 2008 1:40 pm

    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.

  2. August 5, 2013 6:41 am

    Hi there just wanted to give you a quick heads up. The text in your article seem to be running off the screen in Safari. I’m not sure if this is a format issue or something to do with web browser compatibility but I thought I’d post to let you know. The design and style look great though! Hope you get the issue fixed soon. Cheers|

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