- #1
MaestroBach
- 40
- 3
- 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)
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)