Punching Bag Physics: Solving for Impact Force and Acceleration

[jpcoelho]

Dear forum,

I have the following phisics problem. I want to be able to measure the impact of a punch in a regular punching bag. I'm able to measure the acceleration in all the three axis. Besides that I know the punching bag dimensions and weight. The colision between the fist and the bag is not ellastic. Substacial energy is absorbed by the bag. Below I present some pictures of the setup.

I'm looking for the physical differential equations that relates the acceleration and the impact force on the bag. Any help will be appreciated. Regards to all.

 

[mfb]

$$\vec{F}=m\vec{a}$$
You can compare force and acceleration in each dimension separately. This is the acceleration of the center of mass and it neglects the interaction with the pivot (so it is valid only if the timescale of the punch is short enough).
If your accelerometer is not in the center of mass, things can get more complicated.

This is just based on momentum, you don't have to consider energy.

 

[gadong]

This is an interesting problem in applied physics.

It is not trivial, due to the variety of ways in which energy can be transferred (motion of bag, energy absorbed by bag, motion of the boxer).

The maximum angle of displacement of the bag from the vertical direction (after it swings away, like a pendulum from the punch) is a useful parameter as it can be used to compute the energy transferred to the bag (no need to measure acceleration along each axis after the punch).

However, I do not immediately see an easy way to determine how much energy has been absorbed by the bag. The mass of the boxer plays a part in the calculations.

 

[mrspeedybob]

The first question that comes to my mind is what exactly are you trying to measure. "impact of the punch" could mean peak force, average force, impulse, energy, power, or maybe the most useful measure is some other derived unit invented specifically for measuring punches.

What units do you want your results in?

 

[pmacias]

Thank you for bringing this interesting physics problem to the forum. In order to solve for the impact force and acceleration in this scenario, we can use the principle of conservation of momentum and the equations of motion. First, we need to determine the initial velocity of the punching fist before it hits the bag. This can be calculated using the acceleration data and the time it takes for the fist to reach the bag.

Next, we can use the equation of motion, F=ma, to calculate the force experienced by the punching bag. Here, m represents the mass of the punching bag and a represents the acceleration of the bag due to the impact.

To calculate the acceleration of the punching bag, we can use the principle of conservation of momentum, which states that the total momentum before the collision is equal to the total momentum after the collision. By considering the momentum of the punching fist and the punching bag before and after the collision, we can solve for the acceleration of the bag.

It is important to note that the collision between the fist and the bag is not elastic, meaning that some energy is absorbed by the bag. This means that the final velocity of the punching bag will be less than the initial velocity of the fist. Therefore, we can also use the equation for kinetic energy, KE= 1/2mv^2, to calculate the energy absorbed by the bag.

I hope this helps in your problem-solving process. If you need further assistance, please do not hesitate to reach out. Best of luck in solving this physics problem!

Sincerely,