# Determine the change in direction of a particle

• MaestroBach
In summary, the conversation discusses a problem in advanced physics involving the conservation of energy and the change in velocity of a particle moving from z < 0 to z > 0. The person provides a solution using conservation of energy and suggests expressing everything in terms of angles and speed to find the outgoing angle as a function of the incoming angle. The conversation ends with the person realizing they were overcomplicating things.
MaestroBach
Homework Statement
A particle of mass m is moving with velocity*~v*1. It leaves the half-space z <0 in which its potential energy is U1 and enters the half-space z >0 where its potential energy is U2. Determine the change in the direction of the motion of the particle. (Hint: The particle is free in the x and y directions because the potential energy is constant in the (x, y) plane.)
Relevant Equations
Relevant equations: Conservation of momentum, Conservation of energy
Note: I don't know if this actually qualifies as advanced physics, it probably doesn't. It's a review problem in a non-introductory class but I can't solve it so...

Beginning with the hint, I know that the x and y components of velocity don't change when the particle moves from z < 0 to z > 0 because the potential energy is constant in the x,y plane.

Therefore, using conservation of energy I wrote:

U1 + (1/2)mV1^2 = U2 + (1/2)mV2^2, and I substituted v1^2 with (Vx^2 + Vy^2 + Vzo^2) and v2^2 with (Vx^2 + Vy^2 + Vzf^2), where Vzo and Vzf are the initial and final components of velocity in the z direction. After doing some cancelling out, I get

U1 + (1/2)mVzo^2 = U2 + (1/2)mVzf^2

This is where I'm stuck, I don't know where to get another equation from.

(If my notation doesn't make sense ask me, thanks)

Looks good. You can solve it for Vzf, the last unknown.

If you want you can also express everything in terms of angles and speed instead of velocity components, and find the outgoing angle as function of the incoming angle (relative to the x-y-plane).

MaestroBach
mfb said:
Looks good. You can solve it for Vzf, the last unknown.

If you want you can also express everything in terms of angles and speed instead of velocity components, and find the outgoing angle as function of the incoming angle (relative to the x-y-plane).

Haha, thanks, I guess I was overcomplicating things in my head

## 1. What is a particle?

A particle is a small, localized object that has mass and occupies a specific position in space.

## 2. What is the change in direction of a particle?

The change in direction of a particle refers to the difference in the angle or direction of its motion over a period of time.

## 3. How is the change in direction of a particle determined?

The change in direction of a particle can be determined by measuring its initial and final directions, and then calculating the difference between them.

## 4. What factors can cause a change in direction of a particle?

A change in direction of a particle can be caused by various factors such as external forces, collisions, or interactions with other particles.

## 5. Can the change in direction of a particle be predicted?

In some cases, the change in direction of a particle can be predicted by analyzing its initial velocity, mass, and the forces acting upon it. However, there are also instances where the change in direction may be unpredictable due to complex interactions with other particles.

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