Basketball collision with backboard

[Fared]

Hi first post here ,
I am writing an essay on the physics of the basketball shot and I'm stuck on the backboard collision.

As I understand it:
Starting with no spin on the basketball it follows a trajectory path until it reaches the backboard and collides with it. During this collision the basketball slides down the backboard a small distance and some of the linear velocity is changed into angular velocity. I've searched all over but I can't find out how to calculate how far it will slide.

from this site http://archive.ncsa.uiuc.edu/Classes/MATH198/townsend/math.html

I have the equations http://nickhv.com/img/equations.bmp

To tell me the final linear and angular velocities but I don't know how long the ball is in contact with the backboard. I know that

COR = V2(second object) - V2(first object) / V1(first object) - V1(second object)

So if I assume the backboard is immovable and doesn’t absorb any energy,

V2(first object) = COR * V1(first object)

Which leaves me with:

d / t = COR * V1(first object)

If I can find out the distance I can work out the time and substitute that into the original above equations for linear and angular velocity after impact. Or if there is another way to calculate the time the basketball spends in contact with the backboard I would use that. Thanks for your time.

 

[anathema]

Hello,

Thank you for your post and for your interest in the physics of the basketball shot. The backboard collision is an important aspect to consider in understanding the trajectory of a basketball shot.

To start, let's break down the collision into two phases: the initial impact and the sliding phase. During the initial impact, the basketball collides with the backboard and exerts a force on it. This force causes the backboard to deform, and as the backboard recoils back to its original shape, it exerts a force on the basketball. This force acts as a normal force, preventing the basketball from passing through the backboard.

During this initial impact, the time of contact between the basketball and the backboard is very short, on the order of milliseconds. This is because the backboard is relatively rigid and does not deform significantly. Therefore, we can assume that the basketball is in contact with the backboard for a very short amount of time.

Next, let's consider the sliding phase. As you mentioned, some of the linear velocity of the basketball is converted into angular velocity during the collision. This causes the basketball to slide down the backboard a small distance before bouncing off. The distance the basketball slides depends on the coefficient of friction between the basketball and the backboard, as well as the initial velocity of the basketball.

To calculate the distance the basketball slides, we can use the equation d = μNt, where μ is the coefficient of friction, N is the normal force, and t is the time of contact. As we discussed earlier, the time of contact is very short, but we can use an average value for t. The normal force can be calculated using the equation N = mg, where m is the mass of the basketball and g is the acceleration due to gravity.

Once we have the distance the basketball slides, we can then use the equations you mentioned to calculate the final linear and angular velocities. These equations take into account the initial velocity, the coefficient of restitution (COR), and the distance the basketball slides.

I hope this helps you in your essay. If you have any further questions, please feel free to ask. Keep up the curiosity and good luck with your essay!

 

[m2003]

I can provide some insights and suggestions on the physics of a basketball collision with a backboard. The collision between a basketball and a backboard is a complex phenomenon involving both linear and angular motion. In order to understand this collision, we need to consider the forces acting on the basketball and the backboard, as well as the properties of the materials involved.

First, let's look at the forces involved in the collision. When the basketball collides with the backboard, there are two main forces at play - the normal force and the frictional force. The normal force is the force exerted by the backboard on the basketball, perpendicular to the surface of the backboard. This force is responsible for changing the direction of the basketball's motion after the collision. The frictional force, on the other hand, is the force that opposes the sliding motion of the basketball on the backboard. This force is responsible for converting some of the basketball's linear velocity into angular velocity.

Next, let's consider the properties of the materials involved. The backboard is typically made of a rigid material such as glass or acrylic, while the basketball is made of a softer material like rubber. The difference in the elasticity of these materials will affect the amount of energy absorbed during the collision and the resulting motion of the basketball.

Now, let's address the question of calculating the distance the basketball slides down the backboard. This distance will depend on several factors, including the initial velocity and angle of the basketball, the elasticity of the materials, and the time the ball spends in contact with the backboard. As you correctly pointed out, the coefficient of restitution (COR) can be used to relate the velocities before and after the collision. However, determining the time of contact is not a straightforward calculation and may require experimental data or simulations.

In conclusion, the collision between a basketball and a backboard is a complex event that involves various forces and properties of materials. Calculating the distance the basketball slides down the backboard will require considering all these factors and may require experimental data or simulations. I hope this provides some insight into the physics of this phenomenon. Good luck with your essay!