What is the direction of the neutron's velocity after the collision?

In summary, a neutron with a mass of 1.7x10-27 kg and initial velocity of 2.7 km/s collides with a stationary lithium nucleus with a mass of 1.2x10-26 kg. After the collision, the lithium nucleus has a velocity of 0.40 km/s at an angle of 54° to the original direction of motion of the neutron. With a final velocity of 2.5 km/s, the neutron is traveling at an angle of 66° from its initial direction of motion. The equations used to solve for this angle are m1v1x= m1v'1x+m2v'2x and 0= m1v'1
  • #1
oy_katet
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Homework Statement



A neutron (mass 1.7x10-27 kg) traveling at 2.7 km/s hits a stationary lithium nucleus (mass 1.2x10-26 kg). Afterwards, the velocity of the lithium nucleus is 0.40 km/s at 54° to the original direction of the motion of the neutron. If the speed of the neutron after the collision is 2.5 km/s, in what direction is it traveling?

[Answer: 66° from initial direction of neutron's velocity]

Homework Equations



Givens:

m1= 1.7x10-27 kg
v1x= 2.7 km/s

v'1x= (2.5)cosθ
v'1y= -(2.5)sinθ

m2= 1.2x10-26 kg
v2x= 0 km/s

v'2x= (0.4)cos54°
v'2y= (0.4)sin54°

Equations:

m1v1x= m1v'1x+m2v'2x

0= m1v'1y+ m2v'2y

The Attempt at a Solution



I plugged in my values into the two equations, and for the first equation using the x-values I got θ= 65.42° and the second using the y-values I got 65.51°. I was wondering if anyone could point me in the right direction?

I've attached a diagram of my thought process.
 

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  • #2
The values given are probably not very precise, and very probably rounded; they are specified with only two significant digits. Accordingly, you can expect a little "slop" in the results. Believe only two digits, with the second being a bit "fuzzy" :smile:
 

1. What is a collision in two dimensions?

A collision in two dimensions is a type of physical interaction between two objects that have a non-zero relative velocity and impact each other in a two-dimensional space. This can occur in various scenarios, such as objects colliding on a flat surface or in a two-dimensional simulation.

2. How is the momentum conserved in a collision in two dimensions?

Momentum is conserved in a collision in two dimensions through the principle of conservation of momentum. This means that the total momentum of the two objects before the collision is equal to the total momentum after the collision. In two dimensions, this conservation applies separately to the x and y directions.

3. What is the difference between elastic and inelastic collisions in two dimensions?

In an elastic collision, the total kinetic energy of the two objects is conserved, meaning that no energy is lost during the collision. In an inelastic collision, some of the kinetic energy is converted into other forms of energy, such as heat or sound. In two dimensions, both types of collisions can occur depending on the objects and the forces involved.

4. How is the trajectory of objects affected in a collision in two dimensions?

The trajectory of objects can be affected in a collision in two dimensions depending on the angle and velocity of the objects before the collision. The direction and magnitude of the forces involved in the collision can also influence the trajectory. In some cases, the objects may continue moving in the same direction, while in others, their paths may change significantly.

5. What are some real-life examples of collisions in two dimensions?

Some examples of collisions in two dimensions include billiard balls colliding on a pool table, cars crashing into each other at an intersection, or a tennis ball bouncing off a racket. These collisions can also occur in sports such as basketball, where players collide while trying to get the ball, or in air hockey, where players hit the puck back and forth on a flat surface.

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