# Elastic collision of hockey puck

• mybrohshi5
In summary, the two pucks A and B have the same mass and are made of a superball-like material. Puck A initially travels at 15.2 m/s and is deflected 30.0^\circ from its initial direction after striking puck B, which is at rest on a smooth ice surface. The collision is perfectly elastic. Using conservation of momentum and kinetic energy, the final speed of puck A can be found by solving for the directional components of momentum before and after the collision. The conservation of energy equation also gives the angle between the two pucks after collision, which can be used to find the final speed of puck A. However, achieving the correct answer may require multiple attempts.
mybrohshi5

## Homework Statement

Hockey puck B rests on a smooth ice surface and is struck by a second puck A, which has the same mass. Puck A is initially traveling at 15.2 m/s and is deflected 30.0^\circ from its initial direction. The pucks are made of superball-like material, so you may assume that the collision is perfectly elastic.

Find the final speed of the puck A after the collision

## Homework Equations

conservation of momentum for one object at rest (1)
mvai = mvaf + mvbf

conservation of kinetic energy (2)
1/2mvai = 1/2mvaf + 1/2mvbf

## The Attempt at a Solution

I have tried this about 10 times and cannot get it right :(

i solved equation 1 for the x and y components of the velocity final for puck b

vbxf = vaxi - vaxf

vbyf = -vayf

so

vbf = sqrt [(vaxi - vaxf)2 + (-vayf)2]

vbf = sqrt [vaxi2 - 2vaxf + vaxf2 + vayf2]

then i plugged this into 1/2mvai = 1/2mvaf + 1/2mvbf for v_bf

i would show all my steps of reducing but it would take forever.

i end up getting vfa = cos(30) = .866 but this is wrong

am i right up to this point of what i have done?

any help would be great. Thank you

The directional components of momentum before and after are the same. So:

$$mv_{ai} = mv_{af}cos(\alpha) + mv_{bf}cos(\theta)$$ and

$$mv_{af}sin(\alpha) + mv_{bf}sin(\theta) = 0$$

Now the trick is to realize that the conservation of energy equation gives you the angle between the two pucks after collision:

$$v_{ai}^2 = v_{af}^2 + v_{bf}^2$$

so with that angle you can find $\alpha$

AM

## 1. What is an elastic collision?

An elastic collision is a type of collision between two objects where the total kinetic energy of the system is conserved. This means that the objects bounce off each other without any loss of energy.

## 2. How does an elastic collision of a hockey puck occur?

In the case of a hockey puck, an elastic collision occurs when the puck is struck by a hockey stick and bounces off the ice or another object without any loss of energy. This is due to the properties of the materials involved and the conservation of energy and momentum.

## 3. What factors affect the elasticity of a collision?

The elasticity of a collision is affected by several factors, including the materials involved, the velocity and mass of the objects, and the angle at which they collide. In the case of a hockey puck, the hardness and smoothness of the ice also play a role in the elasticity of the collision.

## 4. How is the momentum conserved in an elastic collision of a hockey puck?

Momentum is conserved in an elastic collision of a hockey puck through the exchange of forces between the puck and the stick or other objects involved. The momentum of the puck is transferred to the other object, causing it to move in the opposite direction, while the puck changes direction and continues with its original momentum.

## 5. Can an elastic collision of a hockey puck ever result in a loss of energy?

In theory, an elastic collision should not result in any loss of energy. However, in reality, there may be some small amount of energy lost due to factors such as friction and air resistance. These losses are usually negligible in the case of a hockey puck collision, but they can affect the overall movement of the puck.

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