Off center elastic collision

In summary, the problem involves a mass m1 with a velocity of 11.2m/s that collides off-center with a mass m2=2m1. The final velocities are v1f=a1\hat{i}+b1\hat{j}, and v2f=a2\hat{i}+b2\hat{j}. To obtain the values of a1, a2, and b2, the conservation of momentum equation is used in its vector components form. The solution for b2 is found to be -m1b1/m2. To solve for a1 and a2, the conservation of kinetic energy equation
  • #1
jromeo
1
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Homework Statement



Homework Statement
The mass m1 has the velocity (v1i)\hat{i} and makes an off-center collision with m2=2m1. The final velocities are v1f=a1\hat{i}+b1\hat{j}, and v2f=a2\hat{i}+b2\hat{j}. Assuming elastic collision and v2i=0m/s, obtain the values of a1, a2, and b2 for the given value of b1. Also obtain the angles \theta1 and \theta2 of v1f and v2f with the x-axis. Retain the solutions for a1>0.

m1 = 3.20kg
v1i = 11.2m/s
b1 = 4.12m/s


Homework Equations





The Attempt at a Solution



First I broke down the conservation of momentum equation into it's vector components.
m1v1i = m1a1 + m2a2 and 0 = m1b1 + m2b2. I then solved for b2 by setting b2 equal to
-m1b1/m2. Then I attempted to solve for a1 and a2 by using KEi=KEf because energy is conserved in elastic collisions. KEf = 1/2m1v1i2 = 1/2m1(a12 + b12) + 1/2m2(a22 + b22)

I keep getting the wrong units when I solve for a1 or a2 in one equation though. I can't figure out what I'm missing about this problem. Thanks in advance for any help!
 
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  • #2
Ok your first step is correct however to simplify matters, you can use V1 - V2 = -(V1 - V2) (x and y components of course)

Then solve for either V1 or V2 and plug it into your momentum equations.

Also note that the final angle adds up to 90 degrees
 
  • #3




Based on the information provided, it seems like you are on the right track with your approach. However, it's important to remember that in elastic collisions, both momentum and kinetic energy are conserved. So, the equation you should be using is m1v1i = m1v1f + m2v2f, which takes into account both the final velocities of the two masses.

To solve for a1 and a2, you can use the equation you mentioned, KEi = KEf, which can be written as 1/2m1v1i^2 = 1/2m1v1f^2 + 1/2m2v2f^2. You can then substitute in the values given and solve for a1 and a2.

As for the units, make sure you are using consistent units throughout your calculations. For example, if you are using meters for distance and seconds for time, make sure to use kilograms for mass. If you are still getting incorrect units, double check your calculations and make sure you are using the correct equations.

As for the angles, you can use the equations a1 = v1f*cos(theta1) and b1 = v1f*sin(theta1) to solve for theta1. Similarly, a2 = v2f*cos(theta2) and b2 = v2f*sin(theta2) can be used to solve for theta2.

I hope this helps and good luck with your homework!
 

1. What is an off center elastic collision?

An off center elastic collision is a type of collision where two objects collide with each other, but the point of impact is not directly in the center. This means that the objects will not collide head-on, but at an angle.

2. How is an off center elastic collision different from a center elastic collision?

In a center elastic collision, the two objects collide head-on and their velocities change in opposite directions. In an off center elastic collision, the velocities of the two objects will change in different directions, depending on the angle of impact.

3. What is conserved in an off center elastic collision?

In an off center elastic collision, both momentum and kinetic energy are conserved. This means that the total momentum and total kinetic energy before the collision will be equal to the total momentum and total kinetic energy after the collision.

4. How is the angle of impact in an off center elastic collision determined?

The angle of impact in an off center elastic collision is determined by the direction of the initial velocities of the two objects. The angle of impact can also be calculated using trigonometric functions and the mass and velocities of the objects.

5. What are some real-life examples of off center elastic collisions?

Some real-life examples of off center elastic collisions include a car colliding with a stationary object at an angle, a billiard ball hitting another billiard ball at an angle, or a golf club hitting a golf ball at an angle. These types of collisions can also be seen in sports such as soccer, where players often collide with each other at an angle.

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