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dE_logics

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I derived some values from 2 equations...the values are such that its not complying with one of the equations -

Considering scenario of 2 colliding bodies, in this case both move in the same direction but one is much faster.

u1 = 80

u2 = 500

v1 = ?

v2 = ?

m1 = 100

m2 = 10

Forming equation for law of conservation of K.E -

m1*u1^2 + m2*u2^2 = m1*v1^2 + m2*v2^2

100*6400 + 10*250000 = 100*v1^2 + 10*v2^2

640000 + 2500000 = 100*v1^2 + 10*v2^2

314000 = 10*v1^2 + v2^2...1

Forming equation for law of conservation of Momentum -

m1*u1 + m2*u2 = m1*v1 + m2*v2

8000 + 5000 = 100v1 + 10v2

13000 = 100v1 + 10v2

13000 = 100v1 + 10v2

1300 = 10v1 + v2...2

130 - v2/10 = v1

Substitute v1 in 1 -

314000 = 10*(130 - v2/10)^2 + v2^2

314000 = 10*(16900 + (v2^2)/100 - 26v2) + v2^2

31400 = 16900 + (v2^2)/100 - 26v2 + v2^2

31400 = 16900 - 26v2 + 1.01v2^2

0 = -14500 - 26v2 + 1.01v2^2

0 = 14500 + 26v2 – 1.01v2^2

By quadratic equation formula -

v2 = 107.6364125 and -133.3789860

The negative value will be correct since the body will recoil.

Taking negative value and substituting it in equation 2-

1300 = 10v1 - 133.3789860

v1 = 143.3378986

Taking positive value -

1300 = 10v1 – 107.6364125

v1 = 140.7636412

Error was pointed out by jtbell...and is now fixed.

Considering scenario of 2 colliding bodies, in this case both move in the same direction but one is much faster.

u1 = 80

u2 = 500

v1 = ?

v2 = ?

m1 = 100

m2 = 10

Forming equation for law of conservation of K.E -

m1*u1^2 + m2*u2^2 = m1*v1^2 + m2*v2^2

100*6400 + 10*250000 = 100*v1^2 + 10*v2^2

640000 + 2500000 = 100*v1^2 + 10*v2^2

314000 = 10*v1^2 + v2^2...1

Forming equation for law of conservation of Momentum -

m1*u1 + m2*u2 = m1*v1 + m2*v2

8000 + 5000 = 100v1 + 10v2

13000 = 100v1 + 10v2

13000 = 100v1 + 10v2

1300 = 10v1 + v2...2

130 - v2/10 = v1

Substitute v1 in 1 -

314000 = 10*(130 - v2/10)^2 + v2^2

314000 = 10*(16900 + (v2^2)/100 - 26v2) + v2^2

31400 = 16900 + (v2^2)/100 - 26v2 + v2^2

31400 = 16900 - 26v2 + 1.01v2^2

0 = -14500 - 26v2 + 1.01v2^2

0 = 14500 + 26v2 – 1.01v2^2

By quadratic equation formula -

v2 = 107.6364125 and -133.3789860

The negative value will be correct since the body will recoil.

Taking negative value and substituting it in equation 2-

1300 = 10v1 - 133.3789860

v1 = 143.3378986

**Values do not comply with conservation of K.E**Taking positive value -

1300 = 10v1 – 107.6364125

v1 = 140.7636412

Error was pointed out by jtbell...and is now fixed.

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