# Momentum Calc: Football Player Collisions

• GeoMeo
In summary, the formula for determining force between two objects colliding head-on is momentum = mass x velocity. However, in a collision at an angle, the force is split into two components, one in the same direction and one in the opposite direction. The factor of 1/√2 applies in an ideal situation, but in a collision of equal-sized football players, the impact energy is basically equal regardless of angle. The advantage in a collision comes from being able to tolerate the impact, not from speed or angle. The formula for force is force = mass x acceleration.
GeoMeo
I am trying to determine the formula, (which is momentum?) of 2 objects hitting each other head-on. momentum = mass x velocity (2,000 = 200lbs x 10 mph) times 2 for 4,000. If this is correct, then if one of the masses intersected at say a 45 degree angle, what would the formula be for the force (momentum)?
As you can see I am not a physics kind of guy. I am looking for a practical formula for 2 football players colliding, one at an angle, and how it would compare to a straight on collision. My hope is that the one from the angle could achieve equal or more force with less mass but at a higher velocity then a straight on collision.

The magnitue stays the same. However, momentum is a vector quantity, so in case of a 45 deg. angle collision, part of the momenta of the cars are in the same direction and part in the opposite direction. Each component has magnitude 1/√2 times the magnitude.

The factor of 1/√2 would apply in an ideal situation where, for instance, a race car crumples into a massive teflon-coated concrete barrier at a 45 degree angle. In a collision of equal-sized football players, one would normally model the collision in the center-of-mass frame. That means that there is a half-angle effect at work.

For two players running in the same general direction and converging at a 45 degree angle, each player is running at a 22.5 degree angle relative to the moving center of mass. That means that each player is moving at sin(22.5 degrees) ~= 38% of their running speed relative to the center of mass. Since collision energy scales with the square of relative speed, that's about 15% of the head-on impact energy.

For two players converging at a 135 angle in generally opposite directions, each player is running at a 67.5 degree angle relative to the center of mass. That means that each player is moving at sin(67.5 degrees) ~= 92% of their running speed relative to the center of mass. Square 92% and you get about 85% of the head-on impact energy.

For two players converging at a 90 degree angle they would each be moving at 45 degrees relative to the center of mass. For this situation, the factor of sin(45 degrees) = 1/√2 applies. Square this and you get exactly 50% of the head-on impact energy.

jbriggs444, thanks that was very helpful.
So for equal sized football players the impact energy basically is equal for both regardless of angle. That makes sense even I can understand. If player #1 is 200 lbs and running at 10 mphs and the player #2 is 165 lbs and running at 20 mphs, the impact energy at the center-of-mass stays proportionately the same for both at any angle of impact. Correct?

Thus, player #2 doesn't achieve an advantage by colliding with #1 because of angle.
#2 player can only achieve advantage by increasing his speed to the point that his force is greater then the large #1 player. Correct?

GeoMeo said:
If player #1 is 200 lbs and running at 10 mphs and the player #2 is 165 lbs and running at 20 mphs, the impact energy at the center-of-mass stays proportionately the same for both at any angle of impact. Correct?

Yes. For analysis of the collision, individual speeds don't matter, only the relative speed does. But it would be an over-simplification to think that the way the impact energy is dissipated depends only on the player's relative masses.

Thus, player #2 doesn't achieve an advantage by colliding with #1 because of angle.
#2 player can only achieve advantage by increasing his speed to the point that his force is greater then the large #1 player. Correct?

You are correct that there is no advantage to be had based on angle. But there is also no advantage to be gained by speed. By Newton's third law, the force of the one player on the other is identical to the force of the other player on the one.

A player gains an advantage by arranging matters to that he can tolerate the impact while the opposing player cannot. For instance, by spearing the opponent with helmet on knee.

John exerts enough force on a 30 kg object to cause it to accelerates a 1.75 m/s squared. How much force did he exert? (ignore friction)

Force equals mass times acceleration.
Simples.

## 1. What is momentum and why is it important in football player collisions?

Momentum is a measure of an object's motion, calculated by multiplying its mass by its velocity. In football, momentum is important because it determines the force of impact in collisions between players. A player with a higher momentum will have a greater force and be more difficult to stop.

## 2. How is momentum calculated in football player collisions?

Momentum is calculated by multiplying the player's mass (in kg) by their velocity (in m/s). This can be done using the formula p = m x v, where p represents momentum, m represents mass, and v represents velocity.

## 3. How does momentum affect the outcome of a collision between two football players?

The outcome of a collision between two football players is determined by the difference in their momentums. The player with a higher momentum will have a greater force and will be able to push through or tackle the other player. Momentum also plays a role in determining the direction and speed of the players after the collision.

## 4. Can a player's momentum be changed during a collision?

Yes, a player's momentum can be changed during a collision. This can happen when a player exerts a force on another player, causing their momentum to decrease or change direction. The change in momentum is equal to the force applied multiplied by the time it is applied.

## 5. How can momentum be controlled in football to prevent injuries?

Momentum can be controlled in football by teaching players proper tackling techniques and promoting safe play. Additionally, rules and penalties are in place to prevent players from using excessive force and causing injuries. Proper equipment, such as helmets and padding, can also help to decrease the impact of momentum in collisions.

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