Relativistic momentum football problem

In summary, the conversation discusses a problem involving two football players colliding and sticking together, with one player having a known mass and speed and the other player's speed needing to be calculated. The equation p= mv/[sqrt(1-v^2/c^2)] is used and the answer calculated is 1.94m/s, but this is found to be incorrect when checked against the original equation.
  • #1
Cheezay
26
0

Homework Statement



A football player with a mass of 82.1 kg and a speed of 2.00 m/s collides head-on with a player from the opposing team whose mass is 126 kg. The players stick together and are at rest after the collision. Calculate the speed of the second player, assuming the speed of light is 3.00 m/s

Homework Equations


p= mv/[sqrt(1-v^2/c^2)]


The Attempt at a Solution


Basically how i attempted to solve this is used the above equation for each player, and set them equal to each other using 3.00m/s as the speed of light, because if they are at rest after the collision then their momentum must be equal. Because i have knowns for 1 player, and the mass of the other player, I should be able to solve for v, the other players speed, but the answer i calculate isn't right... any suggestions?
 
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  • #2
First suggestion: show your work in more detail... I don't notice any obvious issues but maybe if you actually specify what you did something will become clear.
 
  • #3
p= 82.1*2/[sqrt(1-2^2/3^2)]
p= 220.297

220.297=126*v/[sqrt(1-(v^2/3^2)]
v= 1.94m/s which is not correct
 
  • #4
Cheezay said:
p= 82.1*2/[sqrt(1-2^2/3^2)]
p= 220.297

220.297=126*v/[sqrt(1-(v^2/3^2)]
v= 1.94m/s which is not correct

Check your answer by putting v=1.94 in the right hand side
(I get 320).
 

FAQ: Relativistic momentum football problem

What is the "Relativistic momentum football problem"?

The "Relativistic momentum football problem" is a thought experiment that explores the effects of special relativity on the momentum of a moving object, specifically a football. It involves a scenario where a football is kicked at near-light speeds and the resulting increase in its mass and momentum due to relativistic effects.

How is momentum affected by special relativity?

According to special relativity, the momentum of an object increases as its velocity approaches the speed of light. This is because the mass of the object also increases, making it more difficult to accelerate and increasing its momentum.

What is the significance of the "Relativistic momentum football problem"?

The "Relativistic momentum football problem" highlights the counterintuitive nature of special relativity and the dramatic effects it has on the behavior of objects moving at high speeds. It also illustrates the importance of considering relativistic effects when studying the motion and interactions of objects in the universe.

Is the "Relativistic momentum football problem" a real-world scenario?

While the "Relativistic momentum football problem" is a hypothetical scenario, it is based on the principles of special relativity which have been tested and confirmed through various experiments and observations. Objects moving at near-light speeds, such as particles in particle accelerators, do experience the effects of relativistic momentum.

What are some potential applications of the "Relativistic momentum football problem"?

The "Relativistic momentum football problem" has implications in fields such as astrophysics, where objects such as neutron stars and black holes can reach near-light speeds. It also has practical applications in particle accelerators and space travel, where understanding relativistic effects is crucial for accurate calculations and predictions.

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