fblin
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Hi everybody some help needed here!
A cube, mass M move with v0 collide with small object "fixed" to the surface in Point P that make it pivot over its side
So far I think I understand:
During the impact there is no conservation of KE
L Angular Momentum : there is an unknown force F (Impulse) on the pivot point
p Linear Momentum : there is a Impulse = F*t in the pivot point (or I should have to consider the mass of the earth)
Known data:
mass M, velocity v0 or v, Side 2a (note that is 2a just for simplification), cm center of mass, rcm vector distance from P to cm, rp distance from P to P (only for completeness)
Before (around Point P of pivot):
\vec{L} = \vec{r_{cm}}\times M\vec{v_{0}}
in this case |r_{cm}||v_{0}|sin(\theta)=av_0
L_{i} = aMv_{0}
After:
\vec{L_{f}} = \vec{r_{p}} \times \vec{F}*t + \vec{r_{cm}} \times M\vec{v_{cm}} +I\vec{\\w}
Where I is the Moment of Inertia of the cube and
v=\\wr_{cm} and r_{cm} = a\sqrt{2}
Note that r_{p} =0 so
L_{f} = 0*F*t + a\sqrt{2}M\\wa\sqrt{2}+I\\w So
L_{i} = L_{f}
aMv_{0} = 2a^2M\\w +I\\w
<br /> \\w = \frac{aMv_{0}}{2a^2M+I}<br />
After the collision It is posible to use Conservation of energy:
E = KE+ V = mgh and KE is 0 and the higher point (the min velocity).
\frac{1}{2}Mv_{cm}+\frac{1}{2}I\\w^2 = Mga(\sqrt{2}-1)
It that ok?
A cube, mass M move with v0 collide with small object "fixed" to the surface in Point P that make it pivot over its side
So far I think I understand:
During the impact there is no conservation of KE
L Angular Momentum : there is an unknown force F (Impulse) on the pivot point
p Linear Momentum : there is a Impulse = F*t in the pivot point (or I should have to consider the mass of the earth)
Known data:
mass M, velocity v0 or v, Side 2a (note that is 2a just for simplification), cm center of mass, rcm vector distance from P to cm, rp distance from P to P (only for completeness)
Before (around Point P of pivot):
\vec{L} = \vec{r_{cm}}\times M\vec{v_{0}}
in this case |r_{cm}||v_{0}|sin(\theta)=av_0
L_{i} = aMv_{0}
After:
\vec{L_{f}} = \vec{r_{p}} \times \vec{F}*t + \vec{r_{cm}} \times M\vec{v_{cm}} +I\vec{\\w}
Where I is the Moment of Inertia of the cube and
v=\\wr_{cm} and r_{cm} = a\sqrt{2}
Note that r_{p} =0 so
L_{f} = 0*F*t + a\sqrt{2}M\\wa\sqrt{2}+I\\w So
L_{i} = L_{f}
aMv_{0} = 2a^2M\\w +I\\w
<br /> \\w = \frac{aMv_{0}}{2a^2M+I}<br />
After the collision It is posible to use Conservation of energy:
E = KE+ V = mgh and KE is 0 and the higher point (the min velocity).
\frac{1}{2}Mv_{cm}+\frac{1}{2}I\\w^2 = Mga(\sqrt{2}-1)
It that ok?
Last edited: