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

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In the discussion about calculating final velocities in a head-on collision, the main focus is on determining the final velocities of two masses after an elastic collision. The initial setup involves a mass m with velocity v0 colliding with a stationary mass 2m. The equations of momentum and kinetic energy are applied, but confusion arises regarding the correct application of these equations, particularly in handling the signs and terms. Participants identify mistakes in the calculations, such as incorrect foiling and the need to include mass terms in the kinetic energy equation. Ultimately, the problem leads to a quadratic equation for the final velocity of the smaller mass, highlighting the complexities involved in collision physics.
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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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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
 
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:
 
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
 
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!)
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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