Collision in two dimensions problems

In summary, we have three identical coins A, B, and C with a diameter of 18.00mm placed on a table in the x,y-plane with coordinates Z(0,0), Y(60.0,0), and X(60.0,45.0) in mm. We are asked to find the angle at which Z should be pushed against Y so that it collides centrally with X after colliding with Y. Assuming an elastic collision and neglecting friction, we can use the equation m1(vi1 - vf1) = m2(vf2 - vi2) and vi1 + vf1 = vf2 + vi2 to solve for the angle without needing to know the velocities. This
  • #1
madlin
1
0
1. On a table (defining the x,y-plane laying 3 identical coins A,B and C with identical diameter of 18.00mm. The coordinates of their centers are Z(0,0), Y(60.0,0), X(60.0, 45.0) all given in mm.
Under what angle relative to the x-axis one has to push Z against Y so that Z performs after the collision with Y another central collision with X?
Assume elastic collision, neglect friction.




2. m1(vi1 - vf1) = m2(vf2 - vi2)
vi1 + vf1 = vf2 + vi2



The Attempt at a Solution


Homework Statement





Homework Equations





3. I really don't understand how to find the angle when we don't have the velocities.
 
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  • #2
Hello madlin.

Increasing the initial speed of Z would be like speeding up a video of the whole process. So, the answer will not depend on the speed.
 

1. What is a collision in two dimensions?

A collision in two dimensions is a scenario where two objects come into contact with each other and their motion is affected by the interaction. This can happen in a variety of situations, such as two cars colliding on a road or two balls colliding in a game of billiards.

2. How do you calculate the momentum of objects involved in a two-dimensional collision?

The momentum of an object is calculated by multiplying its mass by its velocity. In a two-dimensional collision, you must take into account the momentum in both the x and y directions for each object. The total momentum before and after the collision should be equal, according to the law of conservation of momentum.

3. What is the difference between an elastic and inelastic collision?

In an elastic collision, the kinetic energy of the objects involved is conserved before and after the collision. This means that the objects bounce off each other and continue moving. In an inelastic collision, some of the kinetic energy is lost during the collision and the objects may stick together or move in a different direction.

4. How do you determine the final velocities of objects after a two-dimensional collision?

To determine the final velocities of objects after a two-dimensional collision, you will need to use equations that take into account the masses, velocities, and angles of the objects before and after the collision. These equations can be derived from the laws of conservation of momentum and energy.

5. Can you predict the outcome of a two-dimensional collision?

Yes, the outcome of a two-dimensional collision can be predicted using the principles of conservation of momentum and energy. By knowing the initial conditions and properties of the objects involved, you can calculate the final velocities and directions of the objects after the collision. However, external factors such as friction and air resistance may affect the outcome to some extent.

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