Tony Qi

Mar 02, 2022

Curling - Momentum

There are a lot of impacts between rocks in curling(especially when the players are good), and during those impacts, it is always only one rock hitting another one or multiple(if the players are REALLY good). In curling, a new stone can only be thrown once the rock before it has come to a complete stop. Assuming that there is no external force affecting the system, the momentum during the impact of the two rocks will be conserved, while in the real world, the factors that can also affect the system are so minuscule that the system can be considered closed(unless you got hulks’ arms, if that’s you, go save the world instead of curling).

Momentum: momentum by definition is the “motion of the mass” and it can be calculated exactly like that, multiplying the mass of an object and its velocity. 

Conservation of Momentum: We will consider all parts of the following question as a closed system, therefore, the initial total momentum should be the same as the final momentum of the system. 

Elastic Collision: A collision where there is no loss of kinetic energy, therefore both kinetic energy and momentum are conserved in these types of collisions. To help solve elastic collisions, clever people(Like Jerry Zhang) rearranged KEi=KEf and Pi=Pf into one equation:

Inelastic Collision: A collision where kinetic energy is lost, even though kinetic energy is not conserved in inelastic collisions momentum is still conserved. 

Question 2a)Jon and Tony threw a rock with the velocity of 100m/s directly at another rock, both rocks stuck together after the collision, what is the velocity of the two rock systems if they were thrown on an ice surface with negligible friction and negligible air resistance.

Steps to solving:

1, list out the mass and initial velocity of each rock

2, Rewrite total conservation of momentum equation to two rock components 

3, Plug in values using P=mv, since the rock stuck together, the final velocity of the rocks should be the same, and the mass should be the sum of both rocks, 20+20=40kg.

4, Conclusion: The final velocity of the two rocks that stick together should be 50m/s

Question 2b) Jon and Tony threw another rock at the velocity of 50 m/s at another rock, the collision was perfectly elastic, what is the velocity of the rocks after the collision. (they were thrown on an ice surface with negligible friction and negligible air resistance.) 

Steps to solving:

Using the Equation that Jerry,... I mean clever people got us, we can plug our numbers and solve for the final velocity of the desired stone.

Conclusion: The final velocity of the initially moving rock would become 0m/s and the final velocity of the initially at rest rock would become 50m/s. 

Question 2c) Jon and Tony threw their final rock of 100m/s at two rocks placed together, the initial rock struck the centre of the two rocks that are placed right next to each other. One of the rocks went in the direction of 30 degrees to the right of the initial rock’s trajectory at 10m/s, the other, what is the velocity and direction of this rock after the collision? (they were thrown on an ice surface with negligible friction and negligible air resistance.)

Steps to solve:

1, Find initial rocks’ momentum before the collision:

2, Find the two components of rock 2’s momentum”

3, since the original momentum is completely in the y-direction(verticle), the x-direction of the momentum of the third rock should completely cancel out, and the y-direction momentum of the third rock should be the rest of the initial momentum. 

4, Use the two velocity components to find the direction and magnitude of the Final Velocity

5, Convert the total momentum into velocity

6, Therefore, the final velocity of the third rock is 91.48m/s in the direction of 3.13 degrees from the y axis(trajectory of the initial rock)

Those are some generic cases, here is a compilation of actually top-tier takeouts, does conservation of momentum hold up in these situations?