Solving Head-On Collision: Find Ball Speed w/o Knowing Bat Mass

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Discussion Overview

The discussion revolves around solving a physics problem involving an elastic head-on collision between a small superball and a much more massive bat. Participants explore how to determine the speed of the ball after the collision without knowing the mass of the bat, considering the implications of mass ratios and conservation laws.

Discussion Character

  • Exploratory
  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • Some participants note that the mass of the bat is significantly greater than that of the ball, suggesting that the ball's final velocity can be determined independently of the bat's mass under this condition.
  • Others express the need for either the bat's mass or final velocity to solve the problem, indicating uncertainty about how to eliminate these variables.
  • A participant proposes solving the problem using arbitrary values for the bat's mass to observe the behavior of the ball's velocity as the mass increases.
  • Some participants discuss the implications of the conservation of momentum and kinetic energy in elastic collisions, raising questions about the final velocities of both objects.
  • One participant suggests that the bat's final velocity approaches its initial velocity when its mass is much larger than that of the ball, while another participant questions how this occurs.
  • Another viewpoint is presented where the final velocity of the ball is expressed as a function of the mass ratio, indicating that as the mass of the ball approaches zero relative to the bat, the final velocity can be simplified.
  • One participant describes a conceptual approach where the bat is treated as a stationary object, leading to a conclusion about the ball's final velocity based on relative motion.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the necessity of the bat's mass or final velocity for solving the problem. Multiple competing views remain regarding the implications of mass ratios and the application of conservation laws in this context.

Contextual Notes

Some participants express confusion about the mathematical steps involved, particularly in how to handle the mass terms in their equations. There are also unresolved questions about the direction of the bat's final velocity in relation to its initial speed.

daivinhtran
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A small superball of mass m moves with speed v to the right toward a much more massive bat that is moving to the left with speed v. Find the speed of the ball after it makes an elastic head-on collision with the bat. (Use any variable or symbol stated above as necessary.)

In this problem, what is the mass of the bat, exactly?? I spent hours doing this problem, and found no way to solve it without the mass of the bat..
 
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A hint, m_bat is much much greater than m_ball. You will find that the solution for the balls velocity is no longer a function of m_bat when this is the case.
 
MrMatt2532 said:
A hint, m_bat is much much greater than m_ball. You will find that the solution for the balls velocity is no longer a function of m_bat when this is the case.

Yes, I can find the balls velocity is no longer a function of m_bat. However I need the bat final velocity instead.

I need either the bat mass or the bat final velocity to solve the problem. How can I get rid of them?
 
daivinhtran said:
Yes, I can find the balls velocity is no longer a function of m_bat. However I need the bat final velocity instead.

I need either the bat mass or the bat final velocity to solve the problem. How can I get rid of them?

Well the speed of the bat approaches (keyword approaches) its initial speed if m_bat >> m_ball. You would probably expect this.

I suppose what I might suggest is to solve the problem for some arbitrary m_bat. Say m_bat=10*m_ball. Then solve again for 50*m_ball, then 100*m_ball, and so on. You will see that the solution for v_ball approaches some number.
 
You know that this is an elastic collision? Is there any way you can use this fact to give you the info you need?
Also, is are the ball and the bat moving at the same velocity v?
 
thundagere said:
you know that this is an elastic collision? Is there any way you can use this fact to give you the info you need?
Also, is are the ball and the bat moving at the same velocity v?

yes i do know that but...:(
 
MrMatt2532 said:
Well the speed of the bat approaches (keyword approaches) its initial speed if m_bat >> m_ball. You would probably expect this.

I don't get how the speed of the bat can approaches its initial speed after it makes the head-on elastic. Can you please explain more if you don't mind?
 
MrMatt2532 said:
I suppose what I might suggest is to solve the problem for some arbitrary m_bat. Say m_bat=10*m_ball. Then solve again for 50*m_ball, then 100*m_ball, and so on. You will see that the solution for v_ball approaches some number.

I think I got the answer by using this method. Vball = -3v/m
 
MrMatt2532 : Can you confirm my answer please? I only have one last submission on the website.
 
  • #10
daivinhtran said:
I what get how the speed of the bat approaches its initial speed after it makes the head-on elastic. Can you please explain more if you don't mind?
Well can you let me know basically what you have tried so far and where you are currently stuck regarding what I have already said?

I am guessing you have used conservation of momentum and conservation of kinetic energy. From this you have two equations and two unknowns: velocity of the ball after collision and velocity of bat after the collision assuming you know the initial velocities and the masses. Have you gotten to this point? If you have you can try what I initially said which is to try arbitrary masses for the bat that are bigger than the ball or you can look at the equation and see what happens when m_bat gets really large.
 
  • #11
daivinhtran said:
I think I got the answer by using this method. Vball = -3v/m
Yes this is correct. EDIT: what do you mean with the v/m part? The velocity should essentially be 3 times the initial velocity in the opposite direction.
 
  • #12
MrMatt2532 said:
Well can you let me know basically what you have tried so far and where you are currently stuck regarding what I have already said?

I am guessing you have used conservation of momentum and conservation of kinetic energy. From this you have two equations and two unknowns: velocity of the ball after collision and velocity of bat after the collision assuming you know the initial velocities and the masses. Have you gotten to this point? If you have you can try what I initially said which is to try arbitrary masses for the bat that are bigger than the ball or you can look at the equation and see what happens when m_bat gets really large.


I just scanned my work and attached in this reply
 

Attachments

  • #13
MrMatt2532 said:
Yes this is correct. EDIT: what do you mean with the v/m part? The velocity should essentially be 3 times the initial velocity in the opposite direction.


That's what I solved from the two equations.. You can check what I just attached in the previous post...thanks... (we have the m in the problem)


P/s : I don't know how the bat velocity approach its initial speed (as you said)..If that, in what direction?
 
  • #14
I glanced at the work briefly. I think you aren't cancelling out the mass in the numerator and denominator properly. The units of you velocity needs to be a velocity, not a velocity per unit mass.

For example, in the last equation you have written, it should be -299*m*v/(101*m)=-2.96*v
 
  • #15
Also, regarding the bat velocity. Instead of solving for v_ball, you could have solved for v_bat. You should find that v_bat_final equals v_bat_initial in the same direction. Think of a train hitting a bug, the train is not going to slow down whatsoever.
 
  • #16
MrMatt2532 said:
Also, regarding the bat velocity. Instead of solving for v_ball, you could have solved for v_bat. You should find that v_bat_final equals v_bat_initial in the same direction. Think of a train hitting a bug, the train is not going to slow down whatsoever.

THank you so much for having helped me...Now I totally get it...and see the beauty of physics now :D :D
 
  • #17
You can express the final expression for the velocity of the ball as function of M_ball/M_bat. This can be taken as zero as M_ball<<M_bat
 
  • #18
You can get this answer without doing any math at all. Go to coordinate system where the bat isn't moving. The ball approaches it with 2v. Because bat is very massive, it's like hitting a solid wall, so the ball bounces off with -2v. But that's relative to the bat that's moving at -v in problem's coordinate system. That gives you -3v final velocity.
 

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