Question

A professional boxer of mass m1 hits a punching bag in the center of m2 suspended from a cable. The collision between both bodies is perfectly inelastic. Therefore, this combined system is balanced through a height L.

Calculate

a) What is the initial speed of the boxer's fist?

b) If the fist lost all its initial speed when hitting the sack. How high did the sack swing?

c) Find the angular velocity of the bag after the boxer transmitted the full speed of the fist?

You must present the entire procedure and equations to solve this situation.

Answer 1

Solution

a) To solve this problem, we use the linear momentum conservation for perfectly inelastic collision:

(1)

Where:

u₁ and u₂ are the speeds of the bodies before the collision

v₁ and v₂ are the speeds of the bodies after the collision

We assume that the punching bag before the collision is at rest, therefore u2 = 0

(2)

Also, both bodies after the collision, are stuck, therefore, we consider a perfectly inelastic collision, where the final speed for both bodies is the same

Then

(3)

Clearing u₁, we obtain the initial speed of the boxer

(4)

For this case, the kinetic energy of the fist of the boxer was lost during the collision, balancing the punching bag, therefore for a height L, we can use the law of conservation of mechanical energy, as follows:

(5)

So how high the rocking bag was

(6)

c) For a height L, the bag also has rotational kinetic energy, therefore

(7)

where

I: is the inertia momentum of the bag

clearing , the angular speed

(8)