Question on different masses striking balls

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In summary: The balls will have the same velocity after collision and the equation of motion will be:v1 = v2Now take into account the law of conservation of momentum:v1 = v2 - mv1 (where m is the mass of the first ball)Now solve for v1:v1 = (v2 - mv1) / mv1 = (v2 - mv1) / m - 1v1 = (v2 - mv1) / m - 0.5v1 = (v2 - mv1) / m - 0.25
  • #1
s1mondecyrene
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Everybody knows that if a ball hits an equal mass ball the one that was moving will stop and the other on which was stopped will move, this is the funtioning of Newtons craddles.
My question is rather simple:
If a 1kg billiard ball at a speed of 1 m/s hits a 2kg still ball, with what speed will rebound the 1 kg ball? what speed will acquire the 2kg ball? what formula have you used to solve this problem?
 
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  • #2
No external forces => linear momentum is conserved. If it's elastic, then kinetic energy is also conserved. You can derive the necessary formulae from these facts.
 
  • #3
Well i suppose its elastic because the balls rebound and there are neither external forces.
I understand that the moving ball having just half mass than the other it is just able to transfer half of the linear momentum keeping the other half in the rebound.
then the answer would be the 1 kg ball rebounds with a speed of 0.5 m/s and the 2 kg ball would acquire a speed of 0.25 m/s, is this correct?
What I am unable is to figure it out taking into account conservation of energy, just to make sure i did my homework right.
 
  • #4
I would really like to have a number as an answer to my question. The problem our teacher asked us to solve have different more dificult numbers so I will still have to do the work, I put easy numbers to understand it and you could easily solve it. Besides my teacher wouldn't be happy if all i showed him of my work was a number without prior steps
So please is it 0.5 m/s and 0.25 m/s the answer to my question if not what numbers?
 
  • #5
Do not make guess that half of the momentum will be given to the other ball.

Take the velocity of the two balls after collision as v1 and v2 and then write the equation according to law of conservation of momentum.

Other equation between the two unknowns V1 and V2 will come from law of conservation of energy.

solving the two equations you will get actual values of v1 and v2.

First go through the text for collision, this will help you and I am sure there will be some example also.
 

FAQ: Question on different masses striking balls

How does the mass of a ball affect its trajectory when struck?

The mass of a ball does not directly affect its trajectory when struck. The trajectory of a ball is determined by factors such as the angle and velocity of the strike, as well as external forces such as air resistance and gravity.

Does a heavier ball always travel farther when struck with the same force?

Not necessarily. While a heavier ball may have a greater initial force when struck, it also experiences more drag and air resistance, which can slow it down faster than a lighter ball. The distance a ball travels is determined by a combination of its mass, initial force, and external forces acting upon it.

Is there a limit to how much mass can be added to a ball before it becomes too heavy to travel a certain distance?

Yes, there is a limit to how much mass can be added to a ball before it becomes too heavy to travel a certain distance. This is due to factors such as air resistance and the laws of physics. Eventually, the added mass will cause the ball to move too slowly to travel a certain distance.

Can the mass of a ball affect its speed when struck?

Yes, the mass of a ball can affect its speed when struck. A ball with a greater mass will require more force to move it at the same speed as a lighter ball. This is due to the law of inertia, which states that an object with greater mass will require more force to be moved at the same speed as an object with less mass.

Does the mass of a ball affect its bounce when struck?

Yes, the mass of a ball can affect its bounce when struck. A heavier ball will have more momentum and will transfer more energy to the surface it bounces off of, resulting in a higher bounce. However, other factors such as the elasticity of the ball and surface it bounces off of also play a role in the height of the bounce.

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