The discussion centers on the application of the coefficient of restitution in analyzing two-body collisions in both one-dimensional and two-dimensional scenarios. Participants confirm that the relative velocity components can be expressed in terms of x and y coordinates, allowing for a clearer understanding of collision dynamics. Specifically, the coefficient of restitution, denoted as ##e_x##, can be calculated using the velocities of the colliding bodies, factoring in their directional components. The conversation emphasizes the importance of establishing a positive orientation for velocity vectors during collision analysis.
PREREQUISITESStudents studying physics, particularly those focusing on mechanics and collision theory, as well as educators seeking to enhance their teaching methods in these topics.
So, say, if one of the bodies moves along the x axis, and the other moves with an angle of 120 with respect to the horizontal, one can write ##e_x = (v_2cos(120) - v_1)/(u_1 - u_2cos(120)## ?Ssnow said:If collisions are on a line, you can fix a positive orientation of the line so you have positive and negative velocities respect the two opposit directions... it is possible to interpret the minus in front of the vector as a velocity in the opposite sense ...
If the collision is in the plane you can always do the same component by component ...
I don't know if I answered ...
Ssnow
I meant ##e_x## to be the coefficient of restitution. Sorry for not specifying. Anyways, I get it now. ThanksSsnow said:mmmmh, what is ##e_{x}## ? ... if the ##\vec{v}=(v_{1},v_{2})## is the first vector and ##\vec{u}=(u_{1},u_{2})## the second forming an angle of ##120°## then ##\vec{v}=(v_{1},0)## because is on the ##x## axis and ##\vec{u}=(u\cos{(120)},u\sin{(120)})## where ##u## is the magnitude of ##\vec{u}##. Now you must fix a sign ##\pm## to each component that describes the collision ...
Ssnow