Derived values not satisfying equations.

  • Thread starter dE_logics
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In summary, two equations were formed to represent the law of conservation of kinetic energy and momentum in a scenario of two colliding bodies. A quadratic equation was used to solve for the unknown velocities, v1 and v2. After correcting a mistake, the equations were satisfied and the final values for v1 and v2 were found to be 156.3636363636363636 and 500, respectively.
  • #1
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

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.
 
Last edited:
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  • #2
dE_logics said:
314000 = 10*v1^2 + v2^2...1

130 - v2/10 = v1

Substitute v1 in 1 -

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

Do you see your error now?
 
  • #3
Thanks for that man...I edited that question...and the problem still persists after correction.
 
  • #4
I haven't got time to go back over the details right now, but I can suggest a "sanity check." When you solve the quadratic equation to get v2, one of the roots should equal the original u2. This corresponds to the two objects "passing through each other" without interacting, in which case the total momentum and total KE are obviously conserved.
 
  • #5
I think something's wrong with the quadratic equation...the sanity check has failed.

But I don't know what's wrong.
 
  • #6
Problem solved...one of my many careless errors.

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

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

314000 = 169000 + (v2^2)/10 – 260v2 + v2^2

314000 = 169000 – 260v2 + 1.1v2^2

0 = -145000 – 260v2 + 1.1v2^2

0 = +145000 + 260v2 – 1.1v2^2

v2 = 500
v2 = -263.63636363 or -2900/11
alternative -

v1 by eq. 2 = 156.3636363636363636 or 1720/11

Equations satisfied.
 

Related to Derived values not satisfying equations.

1. What are derived values not satisfying equations?

Derived values not satisfying equations are values that are calculated based on other values using an equation or formula, but do not match the expected result. In other words, the calculated value does not follow the rules or principles set by the equation.

2. Why do derived values not satisfy equations?

Derived values may not satisfy equations due to a variety of reasons, such as errors in data input, incorrect equations or formulas, rounding errors, or limitations in the accuracy of measurements.

3. How can derived values not satisfying equations affect scientific research?

When derived values do not satisfy equations, it can lead to incorrect conclusions and potentially impact the validity of the research. It is important for scientists to identify and address any discrepancies in derived values to ensure the accuracy of their findings.

4. What are some ways to troubleshoot derived values not satisfying equations?

To troubleshoot derived values that do not satisfy equations, scientists can double-check their data input, review the equations and formulas used, and perform sensitivity analyses to identify any potential sources of error. They can also consult with colleagues or seek expert advice.

5. How can scientists prevent derived values from not satisfying equations?

Scientists can prevent derived values from not satisfying equations by carefully selecting and testing equations and formulas, using precise and accurate data, and incorporating error analysis techniques to account for any potential discrepancies. It is also important to continuously review and validate all calculations throughout the research process.

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