Boxing gloves are padded to lessen the force of a blow.

Question

(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?

Answer 1

(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.