Analyzing 2D Elastic Collisions with Varying Masses and Velocities

In summary, the conversation discusses an elastic collision between a 1.0-kg particle and a 4.0-kg particle, with the 1.0-kg particle moving in the +x direction at 4.0m/s and the 4.0-kg particle moving in the -x direction at 1.0m/s. After the collision, the 1.0-kg particle moves off at a 130 counterclockwise angle from the positive x-axis. The equations used to solve for the final speeds and directions are also mentioned. The solution strategy involves considering the total momentum vector after the collision and using the center-of-mass system to determine the scattering angle.
  • #1
poolec4
1
0

Homework Statement



A 1.0-kg particle is moving in the +x direction at 4.0m/s when it collides elastically with a 4.0-kg particle moving in the −x direction at 1.0m/s After colliding the 1-kg particle moves off at 130 counterclockwise from the positive x-axis. Find the final speeds of both particles and the direction of the more massive one.

Homework Equations



m1*v1=(m1*v3*cos(ø3))+(m2*v4*cos(ø4))

0=(m2*v4*sinø4)-(m1*v3*sin(ø3))

m1*v1^2 = (m1*(v3)^2) + (m2*(v4)^2)

The Attempt at a Solution



(1 kg)(4i m/s) + (4 kg)(-1i m/s) = 0 ==> The total momentum=0

Is there some sort of trick that can be used for 2 dimensional elastic collisions when the masses and speeds swap? Also, since the total momentum is 0, can it be specified as a center-of-mass system, thus being able to use the scattering angle? Thanks in advance for any help!
 
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  • #2
Hello poolec4. Welcome to PF!

What is the total momentum vector after the collision?

What does that tell you about the magnitudes and the relative directions of the individual final momenta?
 

FAQ: Analyzing 2D Elastic Collisions with Varying Masses and Velocities

What is a 2D elastic collision?

A 2D elastic collision is a type of collision between two objects in a two-dimensional space where both the momentum and kinetic energy are conserved. In an elastic collision, the total kinetic energy before and after the collision remains the same, but the direction and speed of the objects may change.

How is momentum conserved in a 2D elastic collision?

In a 2D elastic collision, the total momentum of the system remains the same before and after the collision. This means that the vector sum of the initial momenta of the two objects is equal to the vector sum of their final momenta.

What is the equation for calculating the velocities of two objects after a 2D elastic collision?

The equation for calculating the final velocities of two objects after a 2D elastic collision is: v1f = ((m1 - m2) * v1i + (2 * m2) * v2i) / (m1 + m2) and v2f = ((2 * m1) * v1i + (m2 - m1) * v2i) / (m1 + m2), where m1 and m2 are the masses of the two objects, and v1i and v2i are their initial velocities.

How does the coefficient of restitution affect a 2D elastic collision?

The coefficient of restitution (e) is a measure of how much kinetic energy is conserved in an elastic collision. In a 2D elastic collision, the value of e ranges from 0 to 1, with 1 representing a perfectly elastic collision where all kinetic energy is conserved, and 0 representing a completely inelastic collision where no kinetic energy is conserved. The higher the value of e, the more elastic the collision is, and the lower the value, the more inelastic the collision is.

What are some real-life examples of 2D elastic collisions?

Some real-life examples of 2D elastic collisions include a game of pool, a game of billiards, a game of air hockey, and a game of ping pong. In all of these games, the collisions between the balls are considered to be elastic, as the momentum and kinetic energy are conserved.

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