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A particle of mass 0.8 kg moving at 4 m/s rebounds of a wall with coefficient of restitution 0.3. How much Kinetic energy is lost?

Coefficient of Restitution (CoR): Speed of Approach x CoR = Speed of Seperation 4 x 0.3 = 1.2 ms -1 Kinetic Energy (KE) Lost: KE lost = Initial KE - Final KE Initial KE = 1/2mv 2 = 1/2 x 0.8 x 4 2 = 6.4 J Fi...
GM
Answered by George M. • Maths tutor
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What is Plato's Analogy of the Cave?

The Analogy of the Cave is a model Plato used in Book VII of The Republic to explain his metaphysical Theory of the Forms It is composed of four key elements:- The sun represents the Form of the Good. Just a...
KM
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How do I conjugate the perfect tense?

In French, the perfect tense is a past tense. It translates to 'I did' or 'I have done'. It is formed by using not one, but two verbs. Perfect tense = subject + auxilary verb + past participle The auxilary i...
HJ
Answered by Harriet J. • French tutor
3786 Views

Show that (n^2) + (n+1)^2 + (n+2)^2 = 3n^2 + 6n + 5, Hence show that the sum of 3 consecutive square numbers is always 2 away from a multiple of 3.

Expanding out the Brackets: (n 2 )+ (n 2 + n + n + 1) + (n 2 + 2n + 2n +4) = (n 2 ) + (n 2 +2n+1) + (n 2 +4n+4) =3n 2 + 6n +5 Using this result: Three consecutice numbers: n, n+1, n+2 So three consecutive sq...
JC
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Solve the pair of simultaneous equations; (1) y + 4x + 1 = 0, (2) y^2 + 5x^2 + 2x = 0 .

Rearrage equation (1) to make y the subject of the formula. This gives y = -4x -1 . Substitute this value of y into equation (2). This gives (-4x -1)^2 +5x^2 +2x = 0 . Expanding out the brackets gives 16x^2 ...
MG
Answered by Melanie G. • Maths tutor
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