Recoil velocity after collision

In summary, to find the recoil velocity of a Cu atom after a collision with a particle of mass 1.00u traveling at speed v, one must use the conservation of momentum equation v = -0.9687v + 62.93u. Solving for u, the recoil velocity of the Cu atom can be expressed as 0.0357v.
  • #1
diffusion
73
0

Homework Statement


A particle of mass 1.00u traveling at speed v, collides with a stationary Cu nucleus of mass 62.93u, and rebounds in the exact opposite direction with a speed of .9687v. What is the recoil velocity of the Cu atom, in terms of v?


Homework Equations


F=ma
P=mv


The Attempt at a Solution


If the recoil of the proton is .9687v and the initial velocity was v, then in order to satisfy conservation of momentum, .0313u/v must be transferred to the Cu atom. To solve for velocity of the Cu atom, use p=mv; 0.0313 = 62.93 x v. Therefore v = 0.0005v.

Am I correct or just going in the completely wrong direction here?
 
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  • #2
Use conservation of linear momentum, you find that the total linear momentum before collision = v
Total linear momentum after collision remains the same and the sum equals v.
Hint : Account for the direction of the particle after collision
 
  • #3
sArGe99 said:
Use conservation of linear momentum, you find that the total linear momentum before collision = v
Total linear momentum after collision remains the same and the sum equals v.
Hint : Account for the direction of the particle after collision

I'm getting the same answer, but still feel like I'm on the wrong track.

Total linear momentum = v = 1.0(.9687) + 62.93(0.00050v).
 
  • #4
diffusion said:

Homework Statement


A particle of mass 1.00u traveling at speed v, collides with a stationary Cu nucleus of mass 62.93u, and rebounds in the exact opposite direction with a speed of .9687v. What is the recoil velocity of the Cu atom, in terms of v?
:cool: What would be the direction of velocity of the particle after the collision?
 
  • #5
diffusion said:
I'm getting the same answer, but still feel like I'm on the wrong track.

Total linear momentum = v = 1.0(.9687) + 62.93(0.00050v).

Wouldn't it be 1.0(.9687 v)? Velocity is a vector, so we have to take into account the direction the body is moving in..
 
  • #6
sArGe99 said:
:cool: What would be the direction of velocity of the particle after the collision?

Negative along x-axis for the proton. Positive for the Cu atom.
 
  • #7
diffusion said:
Negative along x-axis for the proton. Positive for the Cu atom.

Yes.Correct.
So wouldn't one take the velocity of the proton to be negative?
Now, you can write the momentum conservation equation.
 
  • #8
sArGe99 said:
Yes.Correct.
So wouldn't one take the velocity of the proton to be negative?
Now, you can write the momentum conservation equation.

So if the velocity and therefore momentum of the proton is -.9687, the momentum of the Cu particle would have to be... .9687 + .9687 + 0.0313 = 2.2504. Divide by 62.93 = velocity of 0.0357v.

I'm so far off.
 
  • #9
The momentum conservation equation would be
v = -0.9687v + 62.93 u
Express u, the recoil velocity of Cu atom in terms of v. That is the way its found out, I believe.
 

What is recoil velocity after collision?

Recoil velocity after collision refers to the velocity of an object after it collides with another object. It is the speed at which the object moves in the opposite direction of the initial collision.

How is recoil velocity after collision calculated?

Recoil velocity after collision can be calculated using the principle of conservation of momentum, which states that the total momentum of a system remains constant before and after a collision. This can be expressed as: m1v1 + m2v2 = m1v1' + m2v2', where m is the mass of the object and v is its velocity before and after the collision.

What factors affect the recoil velocity after collision?

The recoil velocity after collision is affected by several factors, including the mass and velocity of the objects involved in the collision, as well as the angle and type of collision (elastic or inelastic). Additionally, external forces such as friction can also affect the recoil velocity.

What is the difference between elastic and inelastic collisions?

In an elastic collision, both the momentum and kinetic energy of the objects are conserved, meaning that the total velocity of the objects after the collision is equal to the total velocity before the collision. In an inelastic collision, only the momentum is conserved, and some kinetic energy is lost as heat or sound.

Why is understanding recoil velocity after collision important?

Understanding recoil velocity after collision is important in various fields of science, such as physics and engineering. It allows us to predict the movement of objects after a collision and design structures and machines that can withstand and minimize the effects of recoil. It also helps us understand the behavior of particles and their interactions in the microscopic world.

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