# Collision of Hockey Pucks: Solving for Final Speed and Angle

• ChrisBrandsborg
In summary: The first equation is clearly not correct. That implies ##\theta = 0##. Remember that momentum is a vector so you must respect the direction the object is moving.
PeroK said:
Let's go back to the problem. You found that:

##\cos \theta = \sqrt{\frac{M}{2m}}##

And, I told you something you hopefully already knew, that;

##\cos \theta \le 1##

In order for this scenario to be possible, you must have ##M \le 2m##. If ##M > 2m## it is impossible. With ##M \le 2m## it is possible - that's all we are saying.

Yeah, that´s what I thought :-) Thanks for helping me!

<h2>1. How do you calculate the final speed and angle of two colliding hockey pucks?</h2><p>To calculate the final speed and angle of two colliding hockey pucks, you will need to use the principles of conservation of momentum and conservation of kinetic energy. This involves determining the initial velocities and masses of the pucks, as well as the coefficient of restitution (a measure of the elasticity of the collision). From there, you can use mathematical equations to solve for the final speed and angle.</p><h2>2. What is the coefficient of restitution and how does it affect the collision of hockey pucks?</h2><p>The coefficient of restitution is a measure of the elasticity of a collision. It is a value between 0 and 1, with 1 representing a perfectly elastic collision (where there is no loss of kinetic energy) and 0 representing a completely inelastic collision (where the pucks stick together after the collision). The coefficient of restitution affects the final speed and angle of the pucks after the collision, with a higher value resulting in a more elastic collision and a lower value resulting in a more inelastic collision.</p><h2>3. Can the final speed and angle of the pucks be accurately predicted in a real-life scenario?</h2><p>In a real-life scenario, there are many factors that can affect the final speed and angle of the pucks after a collision, such as friction, air resistance, and imperfections in the surface of the ice. While the mathematical equations used to calculate the final speed and angle can provide a good estimate, there may be slight variations in the actual outcome due to these external factors.</p><h2>4. Does the mass of the pucks play a role in the collision?</h2><p>Yes, the mass of the pucks does play a role in the collision. According to the principle of conservation of momentum, the total momentum of the pucks before and after the collision must be equal. This means that if one puck has a significantly greater mass than the other, it will have a greater effect on the final speed and angle of both pucks after the collision.</p><h2>5. Can the principles used to calculate the collision of hockey pucks be applied to other objects?</h2><p>Yes, the principles of conservation of momentum and conservation of kinetic energy can be applied to the collision of any two objects, not just hockey pucks. These principles are fundamental laws of physics and can be used to analyze the outcome of any type of collision, such as car crashes or billiard balls colliding.</p>

## 1. How do you calculate the final speed and angle of two colliding hockey pucks?

To calculate the final speed and angle of two colliding hockey pucks, you will need to use the principles of conservation of momentum and conservation of kinetic energy. This involves determining the initial velocities and masses of the pucks, as well as the coefficient of restitution (a measure of the elasticity of the collision). From there, you can use mathematical equations to solve for the final speed and angle.

## 2. What is the coefficient of restitution and how does it affect the collision of hockey pucks?

The coefficient of restitution is a measure of the elasticity of a collision. It is a value between 0 and 1, with 1 representing a perfectly elastic collision (where there is no loss of kinetic energy) and 0 representing a completely inelastic collision (where the pucks stick together after the collision). The coefficient of restitution affects the final speed and angle of the pucks after the collision, with a higher value resulting in a more elastic collision and a lower value resulting in a more inelastic collision.

## 3. Can the final speed and angle of the pucks be accurately predicted in a real-life scenario?

In a real-life scenario, there are many factors that can affect the final speed and angle of the pucks after a collision, such as friction, air resistance, and imperfections in the surface of the ice. While the mathematical equations used to calculate the final speed and angle can provide a good estimate, there may be slight variations in the actual outcome due to these external factors.

## 4. Does the mass of the pucks play a role in the collision?

Yes, the mass of the pucks does play a role in the collision. According to the principle of conservation of momentum, the total momentum of the pucks before and after the collision must be equal. This means that if one puck has a significantly greater mass than the other, it will have a greater effect on the final speed and angle of both pucks after the collision.

## 5. Can the principles used to calculate the collision of hockey pucks be applied to other objects?

Yes, the principles of conservation of momentum and conservation of kinetic energy can be applied to the collision of any two objects, not just hockey pucks. These principles are fundamental laws of physics and can be used to analyze the outcome of any type of collision, such as car crashes or billiard balls colliding.

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