The modern boxing glove was introduced in 1743. Before then, gloves weren’t used. Let's assume that the average boxer's arm has a mass of 7 kilograms and reaches 10 m/s before hitting an opponent's face. If upon Collision the face was compressed about three centimeters, what was the force on the opponent's face. (use energy/work analysis) Now with the use of boxing gloves and opponents face compresses 8 centimeters during a below. Solve for the force on the face.
To determine the force on the opponent's face, we can use the principle of work and energy. The work-energy principle states that the work done on an object is equal to the change in its kinetic energy.
1. Without gloves:
Given:
- Mass of the boxer's arm (m) = 7 kg
- Initial velocity (v) = 10 m/s
- Compression distance (d) = 3 cm (converted to meters: 0.03 m)
Step 1: Calculate the initial kinetic energy of the boxer's arm.
The initial kinetic energy (KE) can be calculated using the formula:
KE = 0.5 * m * v^2
KE = 0.5 * 7 kg * (10 m/s)^2
KE = 0.5 * 7 kg * 100 m^2/s^2
KE = 350 joules
Step 2: Calculate the final kinetic energy after compression.
At maximum compression, all the kinetic energy is converted into potential energy.
Thus, the final kinetic energy is zero.
Step 3: Calculate the work done on the opponent's face.
The work done (W) can be calculated as the change in kinetic energy:
W = KE final - KE initial
W = 0 - 350 joules
W = -350 joules
Step 4: Calculate the force on the opponent's face.
The work done is equal to the force multiplied by the compression distance:
W = F * d
-350 joules = F * 0.03 m
F = -350 joules / 0.03 m
F = -11,667 Newtons
Since force cannot be negative, we discard the negative sign. Therefore, the force on the opponent's face without gloves is approximately 11,667 Newtons.
2. With gloves:
Given:
- Compression distance (d) = 8 cm (converted to meters: 0.08 m)
Using the same steps as before, we'll calculate the force on the opponent's face with gloves.
Step 5: Calculate the work done on the opponent's face.
W = F * d
-350 joules = F * 0.08 m
F = -350 joules / 0.08 m
F = -4,375 Newtons
Discarding the negative sign, the force on the opponent's face with gloves is approximately 4,375 Newtons.
Please note that these calculations assume idealized conditions and do not account for factors such as elasticity and real-world dynamics, which can affect the actual forces involved in boxing.
To find the force on the opponent's face, we can use the concept of work and energy.
1. Without gloves:
- The initial kinetic energy of the boxer's arm can be calculated using the formula: KE = (1/2) * mass * velocity^2
- KE = (1/2) * 7 kg * (10 m/s)^2 = 350 J
- The work done on the opponent's face can be calculated as the change in potential energy during the compression of the face: Work = force * distance
- Here, the distance is given as 3 cm, which is equivalent to 0.03 m.
- The work done on the opponent's face is equal to the change in kinetic energy of the boxer's arm, so Work = 350 J.
- Using the formula for work, we can solve for the force: Force = Work / distance
- Force = 350 J / 0.03 m = 11667 N (approximately)
Therefore, the force on the opponent's face without gloves is approximately 11667 N.
2. With gloves:
- Similarly, the initial kinetic energy of the boxer's arm is still 350 J.
- The distance of compression is given as 8 cm, which is equivalent to 0.08 m.
- Using the formula for work, we can again solve for the force: Force = Work / distance
- Force = 350 J / 0.08 m = 4375 N (approximately)
Therefore, the force on the opponent's face with gloves is approximately 4375 N.