# Solve the Ball Collision Problem: Angle α and Friction!

• Copycat91
In summary, the conversation discusses the problem of two identical balls colliding, first in a scenario with no air friction and then in a more realistic scenario with air friction. The solution involves determining the angle at which the thrown ball must be launched in order to collide with the dropped ball. The effect of air friction on the two balls is also considered.
Copycat91

## Homework Statement

Two identical small balls are shown in picture above. A ball is thrown from the ground and another ball is dropped without any initial velocity.
First, consider no air friction. In order to make the balls collide each other, the ball on ground has to make an angle α from the ground, where tan(α)=h/d.
Then consider a more real case, there's air friction which is proportional to ball's velocity, F=-kv. In order to make the balls collide, determine whether angle of the ball has to be greater than α, less than α, or equals to α!

(Problem's source and image: http://collectionofphysicsproblems.blogspot.com" )

Ffriction = -kv
Fgravity = mg

## The Attempt at a Solution

I think it has to be greater than α, is it correct?

Last edited by a moderator:
Welcome to PF.

F = -kv affects which ball the most at t = 0?

The thrown ball, because it has initial velocity, and the other ball doesn't.

Copycat91 said:
The thrown ball, because it has initial velocity, and the other ball doesn't.

Consider both of the components of the velocity at the angle α then of the projectile. If the frictional retarding forces are slowing the projectile in both x,y what will happen if α is left the same? Will it undershoot or over shoot?

Can we consider the initial condition only?
There's also gravitational force and air friction on both balls.
It's hard to imagine...

## 1. What is the "Ball Collision Problem"?

The Ball Collision Problem is a physics-based problem that involves two or more balls colliding with each other. It is commonly used in physics experiments and simulations to study the principles of momentum, energy, and friction.

## 2. How do you determine the angle α in the Ball Collision Problem?

The angle α in the Ball Collision Problem can be determined using the laws of physics, specifically the law of conservation of momentum and the law of conservation of energy. By analyzing the initial and final positions and velocities of the balls, the angle α can be calculated using mathematical equations.

## 3. What role does friction play in the Ball Collision Problem?

Friction plays a significant role in the Ball Collision Problem as it affects the velocity and direction of the balls after the collision. Friction is the force that opposes the motion of the balls and can cause them to lose energy and change their trajectory.

## 4. How does the coefficient of friction impact the outcome of the Ball Collision Problem?

The coefficient of friction is a measure of the amount of friction between two surfaces. In the Ball Collision Problem, a higher coefficient of friction will result in a greater loss of energy and a more significant change in the direction of the balls after the collision.

## 5. Can the Ball Collision Problem be solved using computer simulations?

Yes, the Ball Collision Problem can be solved using computer simulations, which allow for more precise calculations and analysis of the results. These simulations use mathematical models and algorithms to simulate the behavior of the balls and their collisions, taking into account factors such as angle α and friction.

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