A boxer punches a 50 Kg bag. Just as his fist hits the bag, it travels at a speed of 7 m/s. As a result of hitting the bag, his hand comes to a complete stop. Assuming that the moving part of his hand weigh 5 Kg, calculate the rebound velocity and kinetic energy of the bag.
Momentum is conserved. initial momentum of the fist, that has to equal the final momentum of the bag. Calculate its velocity, then its KE.
To solve this problem, we can use the principle of conservation of momentum. According to this principle, the total momentum before the punch is equal to the total momentum after the punch.
Let's denote the velocity of the bag after the punch as Vf, and the final velocity of the boxer's hand as Vh. We can set up the equation as follows:
Total momentum before = Total momentum after
(mass of the bag x initial velocity of the bag) + (mass of the hand x initial velocity of the hand) = (mass of the bag x final velocity of the bag) + (mass of the hand x final velocity of the hand)
(50 kg x 0 m/s) + (5 kg x 7 m/s) = (50 kg x Vf) + (5 kg x 0 m/s)
0 + 35 kg·m/s = 50 kg·Vf + 0
35 kg·m/s = 50 kg·Vf
Now, we can solve for the final velocity of the bag (Vf):
Vf = (35 kg·m/s) / 50 kg
Vf = 0.7 m/s
So, the rebound velocity of the bag is 0.7 m/s.
To calculate the kinetic energy of the bag after the punch, we can use the formula:
Kinetic energy = 1/2 x mass x velocity^2
Kinetic energy of the bag = 1/2 x 50 kg x (0.7 m/s)^2
Kinetic energy of the bag = 1/2 x 50 kg x 0.49 m^2/s^2
Kinetic energy of the bag ≈ 12.25 Joules
Therefore, the rebound velocity of the bag is 0.7 m/s, and the kinetic energy of the bag is approximately 12.25 Joules.
To calculate the rebound velocity and kinetic energy of the bag, we need to use the principles of conservation of momentum and kinetic energy.
First, let's calculate the initial momentum of the boxer's hand before hitting the bag. Momentum is calculated by multiplying mass with velocity. The mass of the boxer's hand is given as 5 Kg, and the velocity is given as 7 m/s.
Initial momentum of the boxer's hand = mass × velocity
= 5 Kg × 7 m/s
= 35 kg·m/s
According to the law of conservation of momentum, the total momentum before and after the collision remains constant. So, when the boxer's hand comes to a complete stop, the bag carries the entire momentum.
Since the final momentum of the bag is equal to the initial momentum of the boxer's hand, we can calculate it using the equation:
Final momentum of the bag = 35 kg·m/s
Next, let's use the concept of kinetic energy to calculate the rebound velocity of the bag. Kinetic energy is given by the equation:
Kinetic energy = (1/2) × mass × velocity^2
The total initial kinetic energy of the system (boxer's hand + bag) is equal to the final kinetic energy of the system after the collision.
Total initial kinetic energy = Final kinetic energy
For the boxer's hand, the initial kinetic energy can be calculated as:
Initial kinetic energy of the hand = (1/2) × mass of the hand × velocity^2
= (1/2) × 5 Kg × (7 m/s)^2
= 122.5 Joules
For the bag, the final kinetic energy can be calculated as:
Final kinetic energy of the bag = (1/2) × mass of the bag × rebound velocity^2
Since the mass of the bag is given as 50 Kg, we can rewrite the equation as:
Final kinetic energy of the bag = (1/2) × 50 Kg × rebound velocity^2
Now, equating the initial and final kinetic energies, we have:
122.5 Joules = (1/2) × 50 Kg × rebound velocity^2
We need to solve this equation to find the rebound velocity of the bag. Rearranging the equation, we get:
rebound velocity = √(122.5 Joules / (0.5 × 50 Kg))
= √122.5 Joules / 25 Kg
= √4.9 m^2/s^2
= 2.21 m/s (approx)
Therefore, the rebound velocity of the bag is approximately 2.21 m/s.
To calculate the kinetic energy of the bag, we substitute the rebound velocity into the equation:
Final kinetic energy of the bag = (1/2) × 50 Kg × (2.21 m/s)^2
= 122.5 Joules
Therefore, the kinetic energy of the bag after the collision is 122.5 Joules.