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. assume the change in mass by removing the glove is negligible. (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) F = 4666.67 N

b) F = 17500 N

c) See it into the explanation.

Explanation:

a) Given info

Mass of the arm, m = 7 Kg

Distance, d = 7.50 cm = 0.075 m

Initial speed, vi = 10.00 m/s

Final speed, vf = 0 m/s

Formulas used:

The work done is calculated by the equation

W = F*d    ⇒   W = - 0.075*F  

where F is the force

The kinetic energy is given by the formula

K = 0.5*m*v²

then

Ki = 0.5*m*vi² = 0.5*(7 Kg)*(10.00 m/s)² = 350 J

Kf = 0.5*m*vf² = 0 J

Calculation:

According to work-energy theorem we get

W = ΔK = Kf - Ki

⇒  - 0.075 m*F = 0 J - 350 J  ⇒  F = 350 J / 0.075 m =  4666.67 N

b) Given info

Mass of the arm, m = 7 Kg

Distance, d = 2.00 cm = 0.02 m

Initial speed, vi = 10.00 m/s

Final speed, vf = 0 m/s

Formulas used:

The work done is calculated by the equation

W = F*d    ⇒   W = - 0.02*F  

where F is the force

The kinetic energy is given by the formula

K = 0.5*m*v²

then

Ki = 0.5*m*vi² = 0.5*(7 Kg)*(10.00 m/s)² = 350 J

Kf = 0.5*m*vf² = 0 J

Calculation:

According to work-energy theorem we get

W = ΔK = Kf - Ki

⇒  - 0.02 m*F = 0 J - 350 J  ⇒  F = 350 J / 0.02 m = 17500 N

c) 17500 N > 4666.67 N

When making use of boxing gloves, the blow will be less painful for both the puncher and the hit. That is, the force of the blow is reduced by the material of the glove.

The gloves reduce the speed of the technique used by the boxer, but also protects them from strong blows.

Larger gloves offer more protection than small ones. The big ones are more padded than the little ones.

Being larger, the force of the blow on the impact takes longer to arrive, thus reducing the impact of the blow.

The force with the glove on is as if a 477 kg (1050 lb) mass were placed on the person’s face. That definitely could do damage, even though it is less than the effective 1790 kg mass of the force with no gloves.

answer: at 24 february, 2014 the population gets twice of its initial population.

explanation:

since we have given that

the population for alpha city, t years after january 1, 2004 is given as

first we find out the initial population, i.e. t=0,

so, our quadratic equation becomes,

according to question, we have said that if the population has twice its initial population, then it becomes

so, time taken to reach this above mentioned population is given by

now, we know that time can't be negative so, we take t=9.149 years.

hence, at 24 february, 2014 the population gets twice of its initial population.

can u provide the graph and if its not possible

then i can tell u the segment where the

average time interval starts degrading is the segment where the car is slowing down