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

• daivinhtran
In summary: I just scanned my work and attached in this...Summary: In summary, the velocity of the ball after it makes the head-on collision with the bat is -3v/m_bat.
daivinhtran
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..

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.

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.

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.

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

• scan0002.pdf
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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?

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

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.

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

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

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.

1. How do you solve a head-on collision involving a ball and a bat without knowing the bat's mass?

In order to solve this type of problem, we can use the principle of conservation of momentum. This principle states that the total momentum of a system remains constant before and after a collision. In this case, we can use the momentum of the ball before and after the collision to calculate the unknown bat mass.

2. What information do we need to solve this type of problem?

In order to solve a head-on collision involving a ball and a bat, we need to know the initial velocity of the ball, the final velocity of the ball, and the mass of the ball. With this information, we can use the conservation of momentum equation to calculate the unknown mass of the bat.

3. What is the equation for conservation of momentum?

The equation for conservation of momentum is: m1v1i + m2v2i = m1v1f + m2v2f where m represents mass, v represents velocity, the subscripts 1 and 2 represent the two objects involved in the collision, and the subscripts i and f represent the initial and final velocities, respectively.

4. Can we solve this problem using other equations or principles?

Yes, we can also use the principle of conservation of energy to solve this type of problem. This principle states that the total energy of a system remains constant before and after a collision. By equating the initial and final kinetic energies of the ball, we can also calculate the unknown mass of the bat.

5. What are some real-life applications of solving head-on collisions?

Solving head-on collisions can be applied in various fields, such as sports, engineering, and physics. In sports, understanding the impact of a bat on a ball can help improve techniques and equipment. In engineering, it can be used to design safer cars and other vehicles. In physics, it can be used to study the conservation of momentum and energy in different scenarios.

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