The next step in finding the total momentum of the ball-floor system is to find the y component of the ball’s momentum immediately before the collision.
To do this, you must first find the y component of the ball’s velocity immediately before the collision. Then, you must find the y component of the momentum immediately before the collision.
To make things easier, you will first assume that the floor is stationary. This is a good assumption to make because you can then take your time finding each quantity, and it will not change with haste. Then, you will compare your answers to see if they are correct.
This article will go into depth about how to find these components and what influences them.
Calculate the mass of both objects
Once you have calculated the velocity of the ball before the collision, you can calculate the momentum of the ball before the collision. Momentum is defined as mass times velocity, so you can calculate the momentum of the ball before the collision by calculating its mass and velocity before the collision.
The mass of both balls is a crucial component of this calculation. If one ball was very heavy, for example, this would change how the balls interact after they collide.
The lighter ball might bounce off of the heavier one instead of being pulled toward it. The difference in mass must be measured accurately to get an accurate answer.
You can now go back to your initial question: what is the y-component of momentum immediately before the collision? You just need to take your answer from above and replace y with -y.
Divide the mass of one object by the other object to find which has the greater mass
Once you have found the velocity of the ball after the collision, you can find the y-component of the momentum of the ball immediately before the collision.
To do this, you will need to divide the mass of one object by the other object to find which has the greater mass. You can then use this mass to find the y-component of one object’s momentum and add it to that object’s current y-velocity to get its new y-velocity.
For example, if we assume that ball A has a mass mA and ball B has a mass mB, then we can write:
yAbefore = yAafter – (vAfter × mB) If we assume that there is no net external force acting on ball A after the collision (which is a fair assumption), then its new velocity will be: vAafter = vAbefore + aYbefore In other words, adding in YBefore gives us YAfter.
Use Newton’s second law to find Pbefore,y
The final piece of the puzzle is to find the y-component of the ball’s momentum immediately before the collision.
You can think of this as “hitting” the ball with an impulse that gives it a certain “y” component of velocity, or how fast and in what direction it is moving across the floor.
To do this, you must again use Newton’s second law: Force = mass x acceleration. You are already familiar with how to find the acceleration, so now you just need to find mass.
Use y = mx + b to find Pbefore,y
Once you have found the x component of the momentum of the ball immediately before the collision (Pbeforex), you can find the y component of the ball’s momentum immediately before the collision (Pbefore,y) by using a simple algebra equation.
You can use any order of operations to do this, but most people use Order Of Operations For Addition And Subtraction.
This is because you first find what value Pbeforex equals, then you find what value y equals, and then you add those values together to get Pbefore,y.
The variable b in this equation is the height of the basketball net above the ground. Because you are finding Pbefore,y in terms of Pbeforex, changing Pbeforex will not change how Pbefore,y turns out.
Check your answers by using P=mv+F and F=ma
Once you have found the y component of the momentum of the ball immediately before the collision, you can find the total force on the ball due to the stick by using a formula that combines Newton’s second law with the y component of momentum.
You can check your answer by calculating how much force was applied by the stick based on how much it slowed down the ball. If your answer is consistent with what would be expected given gravity and how hard you hit the ball, then you did it right!
As mentioned earlier, this method can be difficult because it requires you to know exactly when the stick touches the ball. Even one hundredth of a second off could change your results!
Try practicing several times to see if you get better at detecting when contact occurs between the stick and ball.
Check your answers by using algebraic equations
Once you have the y component of the momentum of the ball immediately before the collision, you can find the total change in y velocity of the ball.
You can do this by subtracting your calculated Pbefore,y from Pcoll,y, which gives you a new momentum for the ball in the y direction. You can then calculate the new y velocity of the ball by using a physics equation called a differential equation.
If there is no net force acting on the ball in any other direction except for down, then this new y velocity will be its new y velocity after the collision. This is very useful to check your answer!
You can also use this new y velocity to find how much time it takes for the ball to fall to ground level after colliding with an object.
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