Three blocks colliding- velocity and angle of the third, so they come to rest

[mmoadi]

Homework Statement

Two blocks (m1 = 0.02 kg, m2 = 0.03 kg, v1 = 1.5 m/s, v2 = 0.5 m/s) are sliding without friction on a surface. They are approaching each other at angle θ = 60º. In what direction and with how much velocity do we have to push the third block (m3 = 0.05 kg) against the first two blocks, so that when they crash they will come to rest?

Homework Equations

p=mv

The Attempt at a Solution

First two blocks:

G(x)= m(2)v(2)*(-sin θ)
G(y)= m(1)v(1) + m(2)*cos θ

Third block:

G(3x)= sin θ

G(3y)= m(1)v(1) – m(2)v(2)*cos θ

For the direction of the third block:

tan θ’= m(2)v(2)*sin θ / m(10v(1) + m(2)v(2)*cos θ → θ’= 19.1º

For the velocity of the third block:

G(3)= m(3)v(3) → v(3)= G3 / m(3)

G3= sqrt(m(1)²v(1)² + m(2)²v(2)² +2m(1)v(1)m(2)v(2)*cos θ)= 0.039686

v(3)= G3 / m(3)= 0.79372 m/s

Are my calculations correct?

 

[anathema]

I appreciate your attempt at solving the problem and your use of the appropriate equations. However, I would like to point out a few things that may help improve your solution:

1. It is important to define your variables clearly. In your solution, it is not clear what G(x), G(y), G(3x), and G(3y) represent. It would be helpful to specify that they are the momentum components in the x and y directions for the first two blocks and the third block, respectively.

2. In your solution, you have used the wrong formula for the momentum of the third block. The correct formula should be G(3) = m(3)v(3)cos θ, since the third block is being pushed at an angle θ.

3. Your calculation for the direction of the third block is incorrect. You have used the wrong formula for tan θ'. The correct formula should be tan θ' = (m(1)v(1) + m(2)v(2)*cos θ)/(m(2)v(2)*sin θ). This gives θ' = 8.13º, not 19.1º.

4. Your calculation for the velocity of the third block is correct, but it would be helpful to specify the units (m/s) for clarity.

Overall, your approach is correct, but there are some errors in your calculations. I would suggest double-checking your equations and using the correct formulas to get the correct solution. Keep up the good work!

 

[kerimek]

I cannot confirm the accuracy of your calculations without reviewing your work and equations in detail. However, your approach seems to be correct and you have used the appropriate equations to solve for the direction and velocity of the third block. I would recommend double-checking your calculations and units to ensure accuracy. Additionally, it may be helpful to provide a diagram or sketch to better visualize the situation.