# Calculating Force on Dog's Head in Collision

• chrotto
In summary, the dog's head is exposed to dangerous forces when it crashes into a stationary object. Because of the dog's small size, the head is getting pinched between the stationary object and its own back part of the body, which we believe is directly behind the head. The forces involved depend on the properties of the head, and the real force is likely larger than the approximation used in the calculation.
chrotto
I am involved in a dispute related to the forces that a dog's head is exposed to when he, of its own power, runs into a stationary object.
Because of the dog's structure (this is a small dog) the head is getting pinched between the stationary object and his own back part of the body (which we believe is directly behind the head).
Let's say the dog's weight is 10 kg and the head hold 20% of the mass and the rest is behind the head. At the collision it would be one force against the forehead from the object and another force toward the back of the head because of the kinetic energy from the 8 kg's that is behind the head. At the same time the parts are linked together.
If I want to calculate the force on the front and back of the head How should I do? Calculate as if it are two separate bodies that collide. First the head with a mass of 2 kg that collied with the solid object and than the back part of the body with a mass of 8 kg that collied with the now stationary head.

I doubt that this calculation will give any meaningful result, but well...

The forces involved in the head->wall crash depend on the properties of the head, especially the time during which the head is decelerated. I would expect that this part is the most dangerous one for the dog.

If the body has mass m, length L and velocity v, the total transferred momentum to stop it is m*v and the maximal time is L/v, giving a minimal average force of mv^2/L. I would expect that the real force is larger.
You can use the same formula as approximation for the head, with stopping distance L' << L.

The question of "An object of mass m hits a surface with speed v and stops. What is the force the surface exerts on the object" recurs here over and over again. But it is impossible to answer because that is not enough information. In order to find the (average) force exerted you would also need to know the time required for the object to come to a stop or the distance it moved (perhaps "crumpled" would be better) as it stopped.

HallsofIvy said:
(perhaps "crumpled" would be better)...

So how much did the dog crumple?

Side question, this mental picture makes me smirk inside. Am I a bad person?

As a scientist, it is important to approach this dispute with a clear understanding of the principles of physics and mechanics. In this situation, it is crucial to consider the concept of force and how it is applied in a collision.

First, we must understand that force is a vector quantity, meaning it has both magnitude and direction. In this case, the force on the dog's head would be the result of the collision with the stationary object. The direction of this force would be towards the back of the head, as the object is pushing against the front of the head.

To calculate the force on the front of the head, we can use the equation F=ma, where F is force, m is mass, and a is acceleration. In this case, the mass of the head is 2 kg, so we can calculate the force by multiplying 2 kg by the acceleration experienced during the collision. To determine the acceleration, we would need to know the speed at which the dog was running and the distance over which the collision occurred.

Similarly, to calculate the force on the back of the head, we would use the same equation but with the mass of the back part of the body (8 kg) and the acceleration experienced by that part of the body during the collision.

It is important to note that the force on the back of the head would likely be greater than the force on the front of the head, as the back part of the body has more mass and therefore would experience a greater acceleration during the collision.

In order to accurately calculate the forces on both the front and back of the dog's head, it is necessary to consider the collision as a single event, rather than two separate collisions. This is because the forces on the front and back of the head are interconnected and affect each other during the collision.

In summary, to accurately calculate the forces on the dog's head during the collision, we must use the principles of mechanics and consider the concept of force as a vector quantity. By treating the collision as a single event and using the equation F=ma, we can determine the forces on both the front and back of the head.

## 1. How do you calculate the force on a dog's head in a collision?

To calculate the force on a dog's head in a collision, you need to know the mass of the dog, the velocity of the collision, and the duration of the collision. The formula for calculating force is F=ma, where F is the force, m is the mass, and a is the acceleration. In a collision, the acceleration can be calculated by dividing the change in velocity by the duration of the collision.

## 2. Why is it important to calculate the force on a dog's head in a collision?

Calculating the force on a dog's head in a collision is important because it helps us understand the potential impact and severity of the collision on the dog. This information can be used to assess the risk of injury or trauma to the dog and inform decisions about safety measures and precautions.

## 3. What factors can affect the force on a dog's head in a collision?

The force on a dog's head in a collision can be affected by several factors, including the mass and size of the dog, the velocity and mass of the object colliding with the dog, and the duration of the collision. Other factors such as the angle and direction of the collision may also play a role.

## 4. Are there any safety precautions that can help reduce the force on a dog's head in a collision?

Yes, there are several safety precautions that can help reduce the force on a dog's head in a collision. These include using safety restraints, such as a harness or crate, while traveling in a vehicle, avoiding high-speed collisions, and using protective gear, such as a helmet, for activities that may involve collisions.

## 5. Can the same method be used to calculate the force on other parts of the dog's body?

Yes, the same method can be used to calculate the force on other parts of the dog's body in a collision. However, it is important to note that different parts of the body may experience different levels of force depending on their location and the direction of the collision. Additionally, the force may be distributed differently throughout the body depending on its structure and composition.

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