Question

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 7.50 cm during a blow in which the 7.00-kg arm and glove are brought to rest from an initial speed of 10.0 m/s. (b) Calculate the force exerted by an identical blow in the days when no gloves were used and the knuckles and face would compress only 2.00 cm. (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) -4667 N

First of all, we can calculate the acceleration of the arm and the glove, using the following equation:

$v^2 - u^2 = 2ad$

where

v = 0 is the final speed

u = 10 m/s is the initial speed

a is the acceleration

d = 7.50 cm = 0.075 m is the distance through which the arm and the glove move before coming to a stop

Solving for a,

$a=\frac{v^2-u^2}{2d}=\frac{0-(10.0 m/s)^2}{2(0.075 m)}=-666.7 m/s^2$

And since the know the mass of the arm+glove:

m = 7.00 kg

We can now calculate the force exerted:

$F=ma=(7.00 kg)(-666.7 N)=-4,667 N$

(b) -17500 N

We can repeat the problem, but this time the stopping distance is different:

d = 2.00 cm = 0.02 m

So the acceleration is

$a=\frac{v^2-u^2}{2d}=\frac{0-(10.0 m/s)^2}{2(0.02 m)}=-2500 m/s^2$

and so the force is

$F=ma=(7.00 kg)(-2500 m/s^2)=-17,500 N$

(c) Yes

The force exerted when the glove is used is

F = 4667 N

We see that this force corresponds approximately to the weight of an object of mass m=476 kg, in fact:

$W=mg=(476 kg)(9.81 m/s^2)=4670 N$

Which is quite a lot. Therefore, the force even when gloves are used seems enough to cause damage.