What is the Maximum Angle of Deflection in a Particle Collision?

AI Thread Summary
The discussion focuses on calculating the maximum angle of deflection for a particle of mass M colliding with a stationary particle of mass m in the center of mass (CoM) frame. The user attempts to establish the relationship between the velocities of the particles before and after the collision, denoting them as u1, u2, u1', and u2'. They express confusion about how to sketch the four vectors representing these velocities in the CoM frame, given that the larger mass is initially at rest. The problem emphasizes the conservation of momentum in the CoM frame, which remains zero before and after the collision. The discussion highlights the complexities of visualizing and calculating the resulting velocities in different reference frames.
fedecolo
Messages
61
Reaction score
1

Homework Statement


A particle of mass ##M## and speed ##v_1## bumps a particle of mass ##m##, ##(M >m)##, at rest. Find the maximum angle of deflection of ##M## after the bump.

The Attempt at a Solution


I would like to solve this problem in the reference frame of the center of mass, because it seems that the counts are very little :D
By definition, if I call ##u_1,u_2## the velocities of the particles in the CdM reference frame, I have ##p_{CdM}=Mu_1 -mu_2=0##. Then I call ##u_1 ',u_2 '## the velocities after the bump (the quantity of motion of Cdm is 0 also after the bump). In the image there is a sketch of the situation, with ##\phi## the scattering angle. But now I'm struggling in relating the velocities ##u_1,u_2,u_1 ',u_2 '## with the end velocities of the particles ##v_1 ', v_2'## in the frame of the laboratory. My question is: how to sketch this four vectors?
 

Attachments

  • IMG_0262.jpg
    IMG_0262.jpg
    6.5 KB · Views: 514
Physics news on Phys.org
In the CoM frame the masses can go in any direction. The problem asks for the frame where the larger mass is initially at rest.
 

Thread 'Errors and significant figures'

I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
View full post »
Thread 'A cylinder connected to a hanging mass'

Thread 'A cylinder connected to a hanging mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
View full post »

Similar threads

Calculate velocities in COM reference frame for 2D collision
Replies
27
Views
1K
Convert to Center of Mass Reference Frame
Replies
9
Views
1K
Calculate the speed and angle of the center of mass before a collision
Replies
3
Views
854
The maximum reversible work in thermodynamics
Replies
22
Views
1K
Proving that mass is an additive quantity
Replies
6
Views
2K
I Determine angle of initial momentum in zero reference frame
Replies
3
Views
1K
Elastic Collision 4: Final Velocities
Replies
4
Views
1K
Maximizing Transferred Energy between n bodies in linear collisions
Replies
3
Views
2K
B Alternative elastic collision formula / physical interpretation
Replies
3
Views
1K
Combining conservation of momentum and kinetic energy
Replies
12
Views
3K

Hot Threads

Recent Insights

Back
Top