Boxing gloves are padded to lessen the force of a blow.
(a) Calculate the force exerted by a boxing glove on an opponent's face, if the glove and face compress 7.00 cm during a blow in which the 8.00 kg arm and glove are brought to rest from an initial speed of 10.0 m/s.
1 N
(b) Calculate the force exerted by an identical blow in the gory old days when no gloves were used and the knuckles and face would compress only 2.00 cm. (Assume the total mass of the arm remains 8.00 kg.)
2 N
(c) Discuss the magnitude of the force with glove on. Does it seem high enough to cause damage even though it is lower than the force with no glove?
(a) We can start by finding the initial kinetic energy of the arm and glove using the formula for the kinetic energy of an object in motion:
KE = (1/2)mv^2
where m = 8 kg is the mass of the arm and glove, and v = 10 m/s is the initial speed.
KE = 0.5 * (8 kg) * (10 m/s)^2 = 400 J
We can find the work done during the compression of the face and glove by finding the average force over the distance compressed (7 cm or 0.07 m). This force will be equal to the work done divided by the distance compressed. Since the arm and glove are brought to rest, all the initial kinetic energy is converted into work done on the person's face. Thus,
W = KE = 400 J
F_avg * d = W
F_avg * 0.07 m = 400 J
F_avg = 400 J / 0.07 m = 5714.29 N
1. Thus, the force exerted by the boxing glove on the opponent's face is about 5714 N.
(b) We can find the force in the old days when no gloves were used similarly. The initial kinetic energy remains the same, but the distance compressed during the blow is now only 2 cm or 0.02 m.
F_avg_old * d_old = KE
F_avg_old * 0.02 m = 400 J
F_avg_old = 400 J / 0.02 m = 20000 N
2. Thus, the force exerted by an identical blow without a glove is 20,000 N.
(c) The magnitude of the force with a glove, 5714 N, is lower than the force without a glove (20,000 N). However, it is still high enough to cause damage because forces of a few thousand Newtons can cause injuries to the tissues and bones in the human body. While the use of gloves reduces the risk of injury, it does not eliminate it entirely.
To solve this problem, we can use the equation for force:
Force = (mass * change in velocity) / time
(a) To calculate the force exerted by a boxing glove on an opponent's face when the glove and face compress 7.00 cm during a blow:
- Mass of the arm and glove (m) = 8.00 kg
- Initial velocity of the arm and glove (v) = 10.0 m/s
- Change in velocity = 0 m/s (since the arm and glove are brought to rest)
- Time taken for the change in velocity (t) = ?
- Compression distance (d) = 7.00 cm
First, let's calculate the time taken for the change in velocity using the equation:
v = u + at
0 = 10.0 - a * t (since final velocity is 0)
From this equation, we find that a * t = 10.0.
Next, let's calculate the acceleration of the arm and glove using the equation:
v^2 = u^2 + 2as
0^2 = 10.0^2 + 2 * a * (-0.07)
From this equation, we find that a = 100.0 m/s^2.
Now, we can substitute the values into the force equation:
Force = (8.00 kg * 0 m/s - 10.0 m/s) / (10.0 / 100.0) = -80.0 N
Since force is a vector quantity, the negative sign indicates that the force is in the opposite direction of the initial velocity. The magnitude of the force is 80.0 N.
(b) To calculate the force exerted by an identical blow in the old days when no gloves were used and the knuckles and face would compress only 2.00 cm:
- Compression distance (d) = 2.00 cm
Using the same equation as before, we can simply substitute the new value of the compression distance:
Force = (8.00 kg * 0 m/s - 10.0 m/s) / (10.0 / 2.00) = -16.0 N
The magnitude of the force is 16.0 N.
(c) Comparing the force with the glove on (80.0 N) and the force with no glove (16.0 N), we see that the force with the glove on is higher. However, even though the force with the glove on is lower than without a glove, it can still cause significant damage due to the compression of the force over a larger distance. The padding in the glove helps spread out the force over a wider area, reducing the likelihood of severe injury.
(a) To calculate the force exerted by a boxing glove on an opponent's face, we can use the principle of conservation of energy.
We need to find the work done on the glove-face system during the compression. This work is equal to the change in kinetic energy of the arm and glove.
The initial kinetic energy of the arm and glove is given by:
KE_initial = (1/2) * mass * velocity^2
Substituting the given values:
mass = 8.00 kg
velocity = 10.0 m/s
KE_initial = (1/2) * 8.00 kg * (10.0 m/s)^2
= 400 J
During the compression, this kinetic energy is converted into potential energy stored in the compressed system:
PE_final = (1/2) * k * x^2
Where k is the spring constant and x is the compression distance.
Given:
Compression distance, x = 7.00 cm = 0.07 m
To find the spring constant, we can use Hooke's Law:
k = F / x
Rearranging the equation, we get:
F = k * x
Now, let's find the spring constant:
k = F_conventional / x_conventional
Where F_conventional = force exerted without gloves
x_conventional = compression distance without gloves
Given:
F_conventional = force exerted by an identical blow without gloves = ?
x_conventional = compression distance without gloves = 2.00 cm = 0.02 m
Using the given information, we will calculate the spring constant without gloves:
(b) Now, let's calculate the force exerted by an identical blow without gloves:
F_conventional = k * x_conventional
Substituting the values:
F_conventional = (42,857.14 N/m) * (0.02 m)
= 857.14 N
(c) To discuss the magnitude of the force with gloves on, we compare it to the force without gloves.
The force with gloves on is given by:
F_gloves = k * x_gloves
Substituting the values:
F_gloves = (42,857.14 N/m) * (0.07 m)
= 3,000 N
Comparing the forces:
F_gloves = 3,000 N
F_conventional = 857.14 N
We can observe that the force exerted with gloves on is significantly higher compared to the force without gloves. Even though the force with gloves is lower, it can still cause damage due to the compression. The padding in the boxing gloves helps to lessen the force and distribute it over a larger area, reducing the risk of serious injuries compared to blows without gloves.