Difference between revisions of "Forest UCM MnAM ElasticCol"

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;Conservation of momentum
 
;Conservation of momentum
  
:<math>m_1 \vec{v}_1 + m_2 \vec{v}_2= m_1 \vec{v}_1^{\prime} +m_2 \vec{v}_2^{\;\;\prime}</math>
+
:<math>m_1 \vec{v}_1 + m_2 \vec{v}_2= m_1 \vec{v}_1^{\prime} +m_2 \vec{v}_2^{\;\prime}</math>
:<math>m_1 \vec{v}_1 = m_1 \vec{v}_1^{\;\prime} +m_2 \vec{v}_2^{\prime}</math>: ball 2 has zero velocity
+
:<math>m_1 \vec{v}_1 = m_1 \vec{v}_1^{\;\prime} +m_2 \vec{v}_2^{\;\prime}</math>: ball 2 has zero velocity
:<math>\vec{v}_1 =  \vec{v}_1^{\;\;\;\prime} + \vec{v}_2^{\prime}</math>: balls have equal masses
+
:<math>\vec{v}_1 =  \vec{v}_1^{\;\prime} + \vec{v}_2^{\;\prime}</math>: balls have equal masses
  
  

Revision as of 12:16, 12 September 2014

An Elastic collision conserves both Momentum and Energy

Pinitial=Pfinal
AND
Einitial=Efinal

Example: problem 3.5

Consider an elastic collision of two equal balls of mass m where one ball has an initial velocity v1 and the remaining ball has zero initial velocity.

Determine the angle between the two balls after the collision.


Conservation of momentum
m1v1+m2v2=m1v1+m2v2
m1v1=m1v1+m2v2: ball 2 has zero velocity
v1=v1+v2: balls have equal masses


Conservation of energy
m_1 v_1^2 + m_2 v_2^2 = m_1 \left(v_1^{\prime}\right)^2 + m_2\left(v_2^{\prime}\right)^2
v_1^2 = \left(v_1^{\prime}\right)^2 + \left(v_2^{\prime}\right)^2



Forest_UCM_MnAM#Elastic_Collision_of_2_bodies