Tony Qi

Mar 02, 2022

Curling - Dynamics

My Chosen sport for this project is Curling, and fun and interesting ways we can do with curling stones outside of the situations of a normal game, such as sending them up ramps or charging them and moving them with electrical force and electric energy. Or more normal things like collisions that happen very regularly in actual games. 

Curling's stones: the stones are the things that are thrown across the ice during games, to keep all of them consistent around the world, all the proper curling stones in the world are manufactured by one factory in Scotland(where curling originated), and each one is an accurate 20kg in mass. 

Curling is full of Dynamics, as we are always pushing rocks across ice sheets with a set initial velocity, and often the game is decided by the thrower’s control over that initial velocity, but I was kind of tired of that, so I instead decide to send the rocks different ramps with different situations, and see how that will turn out. With dynamics on a ramp knowledge from Gr12 Physics, we can calculate how long of a ramp is needed to stop a rock, how far a rock will fly after departing a ramp(along with some Gr11 physics knowledge), and what if we tied two rocks on different ramps to a pulley system. 

Dynamics on a Ramp: objects on a ramp still react the same way to force it would if it was on a flat surface. The most fundamental difference is that when an object is on a ramp, the gravity it experiences would be split into one component, one perpendicular to the surface of the ramp and is responsible for the friction between the object and the ramp, and another part that is parallel to the surface of the ramp and is responsible for the downward pull force that the rock experiences. 

Friction: There will always be friction between two surfaces unless they are perfectly smooth, which doesn’t exist in the real world, it can either be static friction that adds a bottom limit to the amount of force needed to move an object or in our case, a force that always acts against the direction of the object, and both are calculated by taking the coefficient of friction and multiplying it by the normal force the object experiences, but since we are on a ramp, the normal force will only equal the portion of the gravitational force that is perpendicular to the surface of the ramp, instead of the entire gravitational force.

The force acting on the rock: slowing it down/speeding it up, the friction force would always go against the direction of the object’s movement, the rest of the gravitational force would either help pull the rock down if it is going down the ramp, or going against it with the friction force if the rock is going up the ramp. All following the equation:

Kinematics: when objects are travelling with a constant acceleration, kinematics can be used to calculate any one of the following as long as you already have 3 of them: Displacement, initial velocity, final velocity, time, and acceleration. Using these following equations. ⁠

Question 1 a)Tony and Jon Threw a Stone across an ice surface with negligible friction and negligible air resistance with 20m/s of velocity towards a 30 degrees ramp that has a Coefficient of kinetic Friction of 0.45 with the Stone Jon wants the Ramp to be the exact length so that the stone stops at the top of the ramp. How long should the ramp be?

Main Steps to solving:

1, Using trigonometry to separate the gravitational force to its two components parallel and perpendicular to the surface of the ramp. 

2, Calculate the magnitude and direction of the forces applied by the two components to the rock, and the resultant acceleration’s magnitude and direction

Use the acceleration found to find the total distance travelled by the rock with the initial velocity using kinematics. 

Final Conclusion to question 1a):

Therefore, the length of the hypotenuse of the ramp should be 22.94 m in length for the rock to stop right at the top of the ramp.

Question 1b)Tony and Jon threw another rock with the velocity of 100m/s towards a 45-degree angle ramp with the coefficient of kinetic friction of 0.2, the hypotenuse of the ramp is 10m in length, Tony wants to know how far the rock will fly after the end of the ramp?

1, Using trigonometry to separate the gravitational force to its two components parallel and perpendicular to the surface of the ramp. 

2, Calculate the magnitude and direction of the forces applied by the two components to the rock, and the resultant acceleration’s magnitude and direction

1, Calculate the velocity of the rock at the top of the ramp with the known opposing force on the ramp and the initial velocity of the rock. 

2, find the height of the ramp to use to find the time the rock will spend in the air. 

3, in projectile motion, when there is no air resistance, the horizontal direction will not experience any acceleration, and the amount of time the object travels is entirely dependent on the vertical direction of the initial velocity and the gravitational force, using those two variables and kinematics, along with the height of the ramp we found the last step, we will be able to determine the total time the rock spends in the air. 

4, now with the total time spent in the air and the initial velocity in the x-direction we can find the distance the rock will travel horizontally before landing. 

5, Therefore we can conclude that the rock will land 881.08 meters away from the ramp after flying off of it in a projectile motion. 

Question 1c) Jon and Tony built a system where they put two ramps together, one of 30 degrees and coefficient of friction of 0.5 and another of 40 degrees and coefficient of friction of 0.4 degrees, they then attached a pulley to the top of the ramp pyramids and attached two stones to the pulley system, the pulley and string have negligible mass, they pushed the stone on the 30-degree ramp, setting its velocity to 200 m/s at the very beginning, how far would the two rock system travel before they stop.

1, Using trigonometry to separate the gravitational force to its two components parallel and perpendicular to the surface of the ramp. 

2, Calculate the magnitude and direction of the forces applied by the two components to the rock, and the resultant acceleration’s magnitude and direction

Note that in the case of this question, each rock experiences its individual portions of the force, but since they are connected by a pulley, all forces will be collected and applied to the system as a whole, and since the two rocks always experience the same tension force from the pulley in opposite direction, the tension force will always cancel out. 

3, use the total acceleration, the initial velocity, and kinematics to find how far the rock system will travel in its initial direction before stopping. 

4, Therefore, the rock system will travel 4626m in its initial direction before stopping.