Question

As you are walking through a construction zone, you accidentally bump your head against a steel beam. If you are walking at about 1 m/s and if the collision lasted about 0.01 s (so that your head moved about 0.005 m during the collision), what is the average force the beam applies to your head? Assume your head has a mass of 3 kg. If the beam is now padded with about 0.02 m of padding, so that the collision lasts about 0.04 s, what is the average force the padded beam puts on your head?

Answer 1

given
vo = 1 m/s

in the first case,

t1 = 0.01 s, d1 = 0.005 m

let a1 is the acceleration of the head.

use, d1 = vo*t1 + (1/2)*a1*t1^2

0.005 = 1*0.01 + (1/2)*a1*0.01^2

==> a1 = -100 m/s^2

The average force exerted by beam on head, |F_avg| = m*|a1|

= 3*100

= 300 N <<<<<<<<---------------Answer

in the second case,

t2 = 0.04 s, d2 = 0.02 m

let a2 is the acceleration of the head.

use, d2 = vo*t2 + (1/2)*a2*t2^2

0.02 = 1*0.04 + (1/2)*a2*0.04^2

==> a2 = -25 m/s^2

The average force exerted by beam on head, |F_avg| = m*|a2|

= 3*25

= 75 N <<<<<<<<---------------Answer