What ideas have you had so far?
Ball (A) which has mass = m moves along a frictionless horizontal table with velocity
(7i + 5j) it collides with another ball (B) of mass = 4m its velocity is (3i + 3j). Coefficient of restitution is e between the balls. Assume that the common normal at the impact point is the i axis. The balls can be modelled as particles and ignore rotation of the balls.
a) Give 4 eqns relating the velocities of A&B after the collision
b) Determine theses velocities after the collision in terms of the cartesian vectors i & j and e.
c) Why cant the velocity of B after the collison be in the i direction only? Explain?
I am also having trouble with a problem similar to this one: the course I am doing hasn't given any examples in two dimensions in order for me to cross reference or work through, and unfortunately my tutor is away on holiday.
Two of the requested "four equations" I am assuming are for conservation of momentum, and for Newton's law of restitution; but I am at a loss as to what the other two could be!
One idea was simply the expressions of linear momentum for each particle before collision; however, they don't have an expression of velocity after collision. Another idea I had was comparing the kinetic energy before and after collision; but the question asks for this in part d.
If anyone knows of any worked examples somewhere on the web, or is able to provide a nudge in the right direction, I'd be very grateful! - I'm not asking for the answer to the problem; it's just I've spent the past three hours going round in circles, and probably overlooking the very obvious - i'm finding it difficult relating the examples I've been given in the text (one particle is stationary, and one dimension) to this problem!
You should be able to get 2 equations from conservation of linear momentum. State that mass times velocity before impact = mass times velocity after impact. Then solve in the i and j directions.
The third and forth eq.s are from newtons law of restitution. Notice if the i or j direction is parallel to the common normal or the common tangent. . .
Hope this helps . .
and sorry about my lack of math characters!!!