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
The coefficient of restitution, denoted as e, is a measure of the ratio of the final velocity to the initial velocity of two objects after a collision. It is used to describe the elasticity of a collision between two objects.
The coefficient of restitution can be calculated by dividing the final velocity by the initial velocity of the objects involved in a collision. It is represented by the formula e = vf / vi, where vf is the final velocity and vi is the initial velocity.
The coefficient of restitution is significant because it helps to understand the behavior of objects during a collision. It is used to determine whether a collision is elastic or inelastic, with e = 1 representing a perfectly elastic collision and e < 1 representing an inelastic collision.
The coefficient of restitution is applicable in various real-world situations, such as sports like tennis, golf, and billiards. It is also used in engineering and design to determine the impact resistance of materials and to study the dynamics of collisions between objects.
The coefficient of restitution can be affected by various factors such as the type of materials involved in the collision, the shape and surface texture of the objects, and external forces acting on the objects during the collision. Additionally, the temperature and speed of the objects can also impact the coefficient of restitution.