What angle does it scatter at if the yellow ball is scattered

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In summary, the white ball has a speed of 1.37 m/s after the collision and scatter at a angle of 92 degrees.
  • #1
drkidd22
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Homework Statement



The white ball (2kg) in the figure has a speed of 1.74 m/s and the yellow ball (1kg) is at rest prior to an elastic glancing collision. After the collision the white ball has a speed of 1.37 m/s. what angle does it scatter at if the yellow ball is scattered at 280 degrees?


Homework Equations



mva=mvacos(@)+mvbcos(@)

The Attempt at a Solution


2(1.37)Cos(@)a+0.58Cos280
2.74Cos@+.10
=92 degrees

I think I'm close, but not quite.
 
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  • #2


anyone please, a hint?
 
  • #3


drkidd22 said:
mva=mvacos(@)+mvbcos(@)
That's momentum conservation in one direction. What about the other? And what about the fact that the collision is elastic?

The Attempt at a Solution


2(1.37)Cos(@)a+0.58Cos280
2.74Cos@+.10
=92 degrees
I don't understand what you're doing here. I don't see the full equation being used. Where did you get '1.37' and '0.58'? Show all your steps.
 
  • #4


1.37 is given as the speed of ball a after the collision.

0.58 is what I had found the speed of ball b to be after collision, but I think it's not correct as I'm not sure how to really do this problem. I can't really understand what the author of the book is trying to say on a similar problem.
 
  • #5


drkidd22 said:
1.37 is given as the speed of ball a after the collision.
OK.
0.58 is what I had found the speed of ball b to be after collision,
How did you get this? (Hint: That's where the fact that the collision is elastic will come in handy.)
 
  • #6


ok, so I think .58 was incorrect.

mava+mbvb = mava'+mbvb'

2(1.74)+0=2(1.37)+vb'
.74m/s = vb'

Right?
 
  • #7


When I put this in I still don't get the right answer.

2(1.37)Cos(@)+.74Cos280
2.74Cos@+.13
=92.72 degrees
 
  • #8


drkidd22 said:
ok, so I think .58 was incorrect.

mava+mbvb = mava'+mbvb'

2(1.74)+0=2(1.37)+vb'
.74m/s = vb'

Right?
No. That equation isn't valid. (Momentum is a vector--direction matters.)

Instead, make use of the fact that the collision is elastic. What does that mean?
 
  • #9


KE is also conserved
 
  • #10


drkidd22 said:
KE is also conserved
Right! Use that to determine the speed of the yellow ball after the collision.
 
  • #11


3.0276 = 1.8769 + .5(v^2)
(3.0276 - 1.8769)/(.5) = v^2
Vb' = 1.51 m/s
 
  • #12


drkidd22 said:
3.0276 = 1.8769 + .5(v^2)
(3.0276 - 1.8769)/(.5) = v^2
Vb' = 1.51 m/s
Looks good. (I get 1.52, when I round off.)
 
  • #13


0 = 2(1.37)Sin@+1.52Sin280
0 = 2.74Sin@ - 1.50
= 33 degree

I think that's right.

Thanks a million. Took me while to understand it, but I got it. Thanks.
 

What angle does it scatter at if the yellow ball is scattered?

The angle at which the yellow ball scatters depends on a variety of factors, such as the material and shape of the ball, the surface it is scattered on, and the force applied to scatter it. Therefore, there is no specific angle that can be determined without more information.

How is the angle of scattering measured?

The angle of scattering is typically measured using a protractor or other measuring tool. The ball's initial position and the point at which it lands after scattering are measured, and the angle between these two points is calculated.

What is the relationship between the angle of scattering and the energy of the ball?

The angle of scattering is directly related to the energy of the ball. The higher the energy, the greater the scattering angle will be. This is because a higher energy ball will have more force to overcome the surface it is scattered on, resulting in a larger scattering angle.

How does the color of the ball affect the angle of scattering?

The color of the ball does not have a direct impact on the angle of scattering. However, the color may affect the material of the ball, which can in turn affect the scattering angle. For example, a yellow ball made of a softer material may scatter at a different angle than a yellow ball made of a harder material.

Can the angle of scattering be predicted?

The angle of scattering is difficult to predict accurately without specific information about the ball and the surface it is scattered on. However, there are mathematical equations and models that can estimate the angle based on certain parameters, such as the ball's initial velocity and the surface's friction coefficient.

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