When a ball collides with another object, such as a wall or another ball, there is a transfer of momentum. The physics concept of momentum describes the tendency of a moving object to remain moving in a constant direction and velocity.
Velocity is the speed of movement in a constant direction, and acceleration is the change in velocity over time.
Momentum is typically represented by the letter P, and its y-component is represented by the variable y. The y-component of momentum refers to how much momentum has a Y-direction component (towards or away from an object).
When balls collide on a pool table or frisbees collide in the air, there is a transfer of only the y-component of momentum. When two cars collide, however, there is also a transfer of the x- and y-components of momentum.
This article will explain how to find the y-component of the ball’s initial (before) momentume beforethe collision.
Calculate y component of ball’s initial velocity
Now that you have the velocity of the ball immediately before the collision, you can calculate the y component of the ball’s initial velocity.
The y component of the initial velocity is simply the vertical part of the velocity. You can think of it as how fast and in what direction the ball would be moving up or down.
To calculate this, use a simple algebra formula: Ycomp = vx * -1 where vx is the x component of initial velocity and Ycomp is the y component of initial velocity.
This is because in algebra, negative numbers are represented with a downwards arrow. By putting this into your calculation, you are ensuring that only the vertical part of the initial velocity is captured.
Divide the y component of initial velocity by -9.8
Now that you have found the y component of the ball’s momentum immediately before the collision, you can find the y component of the ball’s momentum after the collision.
To do this, you will need to use a different equation. You will need to divide the y component of initial velocity by -9.8, which is exactly what we did in the previous section!
This may seem confusing, but remember that we are dealing with two different situations. In this section, we are taking into account the fact that there is a bounce when hitting the wall, so we have to subtract 9.8 from the y-component of initial velocity. In this section, we are not considering a bounce, so we just take off -9.
Multiply by mass of ball
Once you have found the total before-the-collision momentum of the ball, you can find its y component, or how much it will move in the y direction.
To do this, multiply the total before-the-collision momentum by the mass of the ball. This gives you the before-the-collision momentum of the ball in the y direction.
Put this number into your equation:
y’=yBefore+Pbefore,y where y’ is the displacement in the y direction, yBefore is the displacement in the y direction before the collision, and Pbefore,y is the before-the-collision momentum in the y direction.
This part can be confusing so let’s look at an example. Say you hit a tennis ball with a velocity vector of 10 i•m/s at an angle of 30 degrees above horizontal.
Your hands apply a velocity vector of 12 i•m/s to give it an initial velocity vector of 22 i•m/s.
Because your hands apply a horizontal velocity to it, its after-the collision velocity vector will be only 22 i•m/s in horizontal direction.
To find its displacement after collision in Y direction (up and down), use:
yAfterCollision=yBefore+PbeforeWhere Pbefore is equal to mass times acceleration due to hand velocities applied by hands which is mass*(12i^2). Therefore Y After Collision = Y Before + (mass*(12i^2)).
So In this case Y After Collision = 2 m.
To find its magnitude in x (left and right) directions use: xAfterCollision=xBefore+Pafter Where Pafteris equal to mass times acceleration due to hand velocities applied by hands which is -mass*(-12i^2)). Therefore X After Collison = X Before – (mass * (-12i^2)).
So In this case X After Collison = -1 m.(It goes left 1 meter because it goes down 1 meter.)
(Note that because we are only considering vertical displacement here we did not take into account any possible rotation around either axis.)
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How To Reduce An Object Through A Velocity Component Changes In A Collisions
- : When colliding with an object that has less forward or backward velocity than you do, your whole body will end up having less forward or backward velocity than it did initially.
This happens because your body has more sideways (or lateral) inertia than downward inertia.
“Inertia” just means resistance to change in some variable–in this case, changing velocities.When two objects with different levels of lateral inertia collide, then one object will end up with more lateral (“sideways”) motion than it had initially.
To reduce an object through a “velocity component changes” in a collision , first determine what kind of collisions you are likely to have , then estimate how much damage would occur if your object were to continue moving at its original speed and angle after colliding . Then reduce your speed and angle enough so that damage would be minimal .
More details on how to do this are explained below .
” –Mechanical Engineer Thomas Cappelen , Interviewed by Alex Korpas & Mackenzie Van Volkenburg , The Safest Way To Cross The Street Is Changing Your Velocity., Fast Company , 2019|8|9|https://www.fastcompany.com/9058222/the safest way to cross t he street is changing your velocity..Subtract mass of bat from ball
Now that you have the post-collision velocity of the ball, you can find the y component of the momentum of the ball immediately before the collision.
To do this, subtract the mass of the bat from the ball’s momentum, Pbefore,y, and then subtract its own mass. This gives you an approximation for the momentum of the bat immediately before collision.
You can then plug this into an equation for conservation of linear momentum to find what its y-component is. You can then re-integrate this to find its final post-collision velocity.
You can also do something called a virtual recoil. This is where you take your post-collision velocity and divide it by your approximate mass to get a new force that acts in only one direction: backwards.
Divide x component of momentum by -9.8
Now that you have the x component of the ball’s momentum before the collision, you can find the y component of the ball’s momentum before the collision.
To do this, you will need to divide the x component of momentum by -9.8, which is the velocity of the ball downwards immediately before the collision. You can find this by subtracting the original y-coordinate of the ball from its new y-coordinate.
If you did this correctly, you should get a number that is between -1 and 1. If it is either of these values, then you did it correctly! If it is zero, then you made a mistake in your calculations.
You can now combine these results with those from part one to find out what the y component of momentum is immediately before the collision.
Find the square root of both sides of the equation
Now that you have the y component of the ball’s momentum before the collision, you can find the y component of the ball’s momentum after the collision.
To do this, take the square root of both sides of the equation above. You should get an equation that looks like this:
This new equation tells you that if you know the y component of momentum before a collision (Pbefore,y), then you can find the y component of momentum after a collision (Pafter,y) by taking the square root of Pbefore,y.
For example, say that Pbefore,y = 12 kg·m/s and Pafter,y = 7 kg·m/s.
Take the inverse cosine of both sides of the equation using a calculator or computer program
To find the y component of the momentum of the ball immediately before the collision, take the inverse cosine of both sides of the equation Pbefore,y=mvbefore,sinθ.
This gives you Pbefore,y=mvbefore,sinθ where vbefore is the y component of velocity and m is mass. You can now plug in vbefore and sinθ to get your answer!
You can also use this formula to find out what the y component of momentum of the ball immediately before the collision is. By taking the inverse cosine of both sides of Pbefore,y=Pafter,y you can find out what Pafter,y is.
Be careful when doing this calculation as it is easy to make a mistake with these equations.
Round to two places after the decimal point
Now that you have the y component of the ball’s momentum before the collision, you can find the y component of the ball’s momentum after the collision.
To do this, you will need to take the dot product of your x and y components of initial momentum with respect to time. You will then need to multiply this by your time interval and then subtract your y component of initial momentum with respect to time.
You will then have your final answer!
For example, let’s say that the initial velocity of the ball was 2 m/s (or 2 knots) in a direction 5 degrees below horizontal. The ball strikes a wall that is 2 m high at an angle of 45 degrees above horizontal.
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