Asst 23 Query

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course phy 201

Aug 1 4:15pm

If your solution to stated problem does not match the given solution, you should self-critique per instructions at http://vhcc2.vhcc.edu/dsmith/geninfo/labrynth_created_fall_05/levl1_22/levl2_81/file3_259.htm.

 

Your solution, attempt at solution. If you are unable to attempt a solution, give a phrase-by-phrase interpretation of the problem along with a statement of what you do or do not understand about it. This response should be given, based on the work you did in completing the assignment, before you look at the given solution.

 

023. `query 23

 

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Question: `q Query gen phy 7.27 bumper cars 450 kg at 4.5 m/s, 550 kg at 3.7 m/s, collision from back, elastic

 

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Your solution:

 

 

m1 v1 + m2 v2 = m1 v1' + m2 v2' and v2 - v1 = -( v2' - v1')

450 kg * 4.5 m/s + 550 kg * 3.7 m/s = 450 kg * v1 ' + 550 kg * v2

4060 kg m/s = 450 kg * v1 ' + 550 kg * v2

406 m/s = 45 v1 ' + 55 v2

3.7 m/s - 4.5 m/s = -(v2 ' - v1 ' )

v1 ' = v2 ' - .8 m/s

406 m/s = 45 ( v2 ' - .8 m/s) + 55 v2

v2 ' = 4.42 m/s

v1 ' = 4.42 m/s - .8 m/s = 3.62 m/s

pAfter = 450 kg * 3.62 m/s + 550 kg * 4.42 m/s = 4060 m/s

m1 v1 ' - m1 v1 = 450 kg * 3.62 m/s - 450 kg * 4.5 m/s = - 396 kg m/s

406 m/s = 45 ( v2 ' - .8 m/s) + 55 v2 '

406 m/s = 45 v2 ' - 36 m/s + 55 v2 '

406 m/s = -36 m/s + 100 v2 '.

442 m/s = 100 v2 '

v2 ' = 442 m/s / 100 = 4.42 m/s

 

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Given Solution:

`a** For an elastic collision we have m1 v1 + m2 v2 = m1 v1' + m2 v2' and v2 - v1 = -( v2' - v1').

 

We substitute m1, v1, m2 and v2 to obtain

 

450 kg * 4.5 m/s + 550 kg * 3.7 m/s = 450 kg * v1 ' + 550 kg * v2 ', or

 

4060 kg m/s = 450 kg * v1 ' + 550 kg * v2 ' . Dividing by 10 and by kg we have

406 m/s = 45 v1 ' + 55 v2 '.

 

We also obtain

 

3.7 m/s - 4.5 m/s = -(v2 ' - v1 ' ) or

v1 ' = v2 ' - .8 m/s.

 

Substituting this into 406 m/s = 45 v1 ' + 55 v2 ' we obtain

 

406 m/s = 45 ( v2 ' - .8 m/s) + 55 v2 ' . We easily solve for v2 ' obtaining

 

v2 ' = 4.42 m/s. This gives us

v1 ' = 4.42 m/s - .8 m/s = 3.62 m/s.

 

Checking to be sure that momentum is conserved we see that the after-collision momentum is

 

pAfter = 450 kg * 3.62 m/s + 550 kg * 4.42 m/s = 4060 m/s.

 

The momentum change of the first car is m1 v1 ' - m1 v1 = 450 kg * 3.62 m/s - 450 kg * 4.5 m/s = - 396 kg m/s.

 

The momentum change of the second car is m2 v2 ' - m2 v2 = 550 kg * 4.42 m/s - 550 kg * 3.7 m/s = + 396 kg m/s.

 

Momentum changes are equal and opposite.

 

NOTE ON SOLVING 406 m/s = 45 ( v2 ' - .8 m/s) + 55 v2 ' FOR v2 ':

 

Starting with

 

406 m/s = 45 ( v2 ' - .8 m/s) + 55 v2 ' use the Distributive Law to get

406 m/s = 45 v2 ' - 36 m/s + 55 v2 ' then collect the v2 ' terms to get

406 m/s = -36 m/s + 100 v2 '. Add 36 m/s to both sides:

442 m/s = 100 v2 ' so that

v2 ' = 442 m/s / 100 = 4.42 m/s. *

 

STUDENT NOTE AND INSTRUCTOR RESPONSE:

 

Ok i wasnt sure about the formulas which are:m1 + v1 + m2 + v2 = m1 + v1' + m2 + v2'and v2 -v1 = -(v2' - v1')
INSTRUCTOR RESPONSE:  Those are the formulas, except that you don't have any * in the first (* should replace two of your + signs; should read m1 * v1 + m2 * v2 = m1 * v1' + m2 * v2' or just m1 v1 + m2 v2 = m1 v1' + m2 v2'). Note that the units of m1 and v1, for example, make it impossible to add m1 and v1.
The meaning of the formulas is simpler and easier to remember than the formulas. If you understand the meaning you can always reconstruct the formulas:
For an elastic collision:

• Total momentum after = total momentum before.

• Relative velocity reverses (i.e., relative velocity after collision is equal and opposite to relative velocity before collision).

Recall that an elastic collision is one in which both momentum and kinetic energy are conserved. The formulas are straightfoward:
m1 v1 + m2 v2 = m1 v1' + m2 v2' and1/2 m1^2+ 1/2 m2 v2^2 = 1/2 m1 v1'^2 1/2 m2 v2'^2.
The second formula is more complicated than v2 - v1 = - (v2' - v1'), which combined with the first formula gives us the same results, so we use this formula instead of the second.

 

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Self-critique (if necessary):

 

 

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