Calculating Final Velocities in a Head-On Collision | Physics Homework Solution

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In summary, the conversation discusses a collision between two masses, one with an initial velocity and the other at rest. The goal is to find the final velocities of both masses as ratios to the initial velocity. The equations used are conservation of momentum and kinetic energy. However, there are errors in the attempt at a solution, including using the wrong sign for the second velocity, not including the masses in the kinetic energy equation, and making a mistake in simplifying the equation. The correct solution involves solving a quadratic equation.
  • #1
kraigandrews
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Homework Statement


A mass m with initial velocity v0 collides head on with a mass 2m initially at rest. What is the final velocity of the smaller mass, as a ratio to v0?

What is the final velocity of the larger mass, as a ratio to v0?



Homework Equations



Pi=Pf

KE=.5mv^2

The Attempt at a Solution



for part a I am confused as to what I am doing wrong:

mvo=mv1+2mv2
it wants to find v1 in terms of vo so:

v2=.5(vo+v1)

then plug into KE equation:

vo2=v12+.25(v12+vo2)
and simplify to get

(3/4)vo2=(5/4)v12

then v1=(3/5)1/2vo
 
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  • #2
kraigandrews said:
for part a I am confused as to what I am doing wrong:

mvo=mv1+2mv2
it wants to find v1 in terms of vo so:

v2=.5(vo+v1)
That + should be minus.


ehild
 
  • #3
hi kraigandrews! :smile:
kraigandrews said:
mvo=mv1+2mv2
it wants to find v1 in terms of vo so:

v2=.5(vo+v1)

then plug into KE equation:

vo2=v12+.25(v12+vo2)
and simplify to get

(3/4)vo2=(5/4)v12

then v1=(3/5)1/2vo

hmm …

i] v2=.5(vo minus v1)

ii] you need to put m or 2m in the KE equation

iii] (vo+v1)2 is not v12+vo2 :redface:
 
  • #4
yeah wow that was a dumb mistake not foiling, for the KE part I just canceled the masses:

but now I am left with
(3/4)Vo^2=(5/4)V1^2-(1/2)Vo*V1
and I am not quite sure how to solve this for V1
 
  • #5
erm :rolleyes: … it's a quadratic equation! :smile:

(and anyway, v0 = v1 is obviously going to be a solution, since that corresponds to the masses not colliding!)
 

FAQ: Calculating Final Velocities in a Head-On Collision | Physics Homework Solution

1. How do you calculate the final velocity in a head-on collision?

In a head-on collision, the final velocity can be calculated using the formula: Vf = (m1v1 + m2v2) / (m1 + m2), where Vf is the final velocity, m1 and m2 are the masses of the objects involved, and v1 and v2 are the initial velocities of the objects.

2. What is the conservation of momentum and how does it apply to head-on collisions?

The conservation of momentum states that in a closed system, the total momentum remains constant. In a head-on collision, the total momentum before the collision is equal to the total momentum after the collision. This means that the sum of the initial velocities of the objects is equal to the sum of the final velocities.

3. Can you calculate the final velocity if the masses and initial velocities are unknown?

No, the final velocity cannot be calculated if the masses and initial velocities are unknown. In order to use the formula, you need to know at least two of the three variables (final velocity, masses, and initial velocities).

4. Are there any assumptions made when calculating final velocities in a head-on collision?

Yes, there are some assumptions made when calculating final velocities in a head-on collision. These include assuming that there is no external force acting on the objects, there is no energy lost during the collision, and the collision is elastic (the objects bounce off each other).

5. How do you determine the direction of the final velocities in a head-on collision?

The direction of the final velocities in a head-on collision can be determined by using the law of conservation of momentum. The final velocities will have the same direction as the initial velocities, but the signs may change depending on the masses and initial velocities of the objects involved.

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