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 gory old 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?

Short answer

(a) The force exerted by a boxing glove on an opponent’s face is 4666.67N.

(b) The force exerted when no gloves are used is 17500N.

(c) The magnitude of the force with gloves on is enough to damage the face.

Step-by-step solution

Definition of Concept 

Third law of motion: According to the third law of motion, every action has equal but opposite reaction force.

Suppose body A exerts a force$F_{AB}$on another body B, then according to Newton’s third law body B also exert the force$F_{AB}$on body A which is,

$F_{AB}=-F_{AB}$

Force exerted on opponent’s face with gloves on

(a)

According to work energy theorem,

$\begin{array}{rcl}W& =& \frac{1}{2}m{v}^2-\frac{1}{2}m{u}^2\\ F_{g}s& =& \frac{1}{2}m{v}^2-\frac{1}{2}m{u}^2\end{array}$

Here,$F_g$is the force exerted on the gloves,m is the mass of the arm ,v is the final velocity of the gloves ($v=0$as the gloves comes to rest after hitting opponent’s face), u is the initial velocity of the gloves$\left(u=10\text{m}/\text{s}\right)$, and s is the distance covered by the gloves before it comes to rest$\left(s=7.5\text{cm}\right)$.

The expression for the force exerted on the gloves is,

$F_g=\frac{m\left(v^2-u^2\right)}{2s}$

Putting all known values,

$\begin{array}{rcl}{F}_g& =& \frac{\left(7\text{kg}\right)\times \left[{\left(0\right)}^2-{\left(10\text{m}/\text{s}\right)}^2\right]}{2\times \left(7.5\text{cm}\right)}\\ & =& \frac{\left(7\text{kg}\right)\times \left[{\left(0\right)}^2-{\left(10\text{m}/\text{s}\right)}^2\right]}{2\times \left(7.5\text{cm}\right)\times \left(\frac{1\text{m}}{100}\right)}\\ & =& -4666.67\text{N}\end{array}$

According to the Newton’s third law of motion, the force exerted by gloves on opponent’s face is,

$F_f=-F_g$

Putting all known values,

$\begin{array}{rcl}{F}_f& =& -\left(-4666.67\text{N}\right)\\ & =& 4666.67\text{N}\end{array}$

Therefore, the required force exerted by the gloves on the opponent’s face is 4666.67 N.

Force exerted on the opponent’s face when no gloves are used

(b)

According to work energy theorem,

$$\begin{gathered} W\text{'}=\frac{1}{2}mv{\text{'}}^2-\frac{1}{2}mu{\text{'}}^2 \\ {F}_{k}s\text{'}=\frac{1}{2}mv{\text{'}}^2-\frac{1}{2}mu{\text{'}}^2 \end{gathered}$$

Here,is the force exerted on knuckles,m is the mass of the arm $\left(m=7\text{kg}\right)$,$v\text{'}$is the final velocity of the knuckles (as the knuckles comes to rest after hitting opponent’s face),$u\text{'}$is the initial knuckles of the gloves$\left(u\text{'}=10\text{m}/\text{s}\right)$, and$s\text{'}$is the distance covered by the knuckles before it comes to rest$\left(s\text{'}=2\text{cm}\right)$.

The expression for the force exerted on the knuckles is,

$F_k=\frac{m\left({v\text{'}}^2-{u\text{'}}^2\right)}{2s\text{'}}$

Putting all known values,

$\begin{array}{rcl}{F}_k& =& \frac{\left(7\text{kg}\right)\times \left[{\left(0\right)}^2-{\left(10\text{m}/\text{s}\right)}^2\right]}{2\times \left(\text{2 cm}\right)}\\ & =& \frac{\left(7\text{kg}\right)\times \left[{\left(0\right)}^2-{\left(10\text{m}/\text{s}\right)}^2\right]}{2\times \left(\text{2 cm}\right)\times \left(\frac{1\text{m}}{100}\right)}\\ & =& -17500\text{N}\end{array}$

According to the Newton’s third law of motion, the force exerted by knuckles on opponent’s face is,

$F{\text{'}}_f=-F_k$

Putting all known values,

$\begin{array}{rcl}F{\text{'}}_f& =& -\left(-17500\text{N}\right)\\ & =& 17500\text{N}\end{array}$

Therefore, the required force exerted by the knuckles on the opponent’s face is 17500N.

The magnitude of force on gloves

(c)

When the boxing gloves are used, the force is considerably reduced than that with the knuckle punch. Even though with the gloves the force is enough to cause the damage to the opponent’s face.