Occupants of cars hit from behind, even at low speed, often suffer serious neck injury from whiplash. During a low‑spee rear‑end collision, a person's head suddenly pivots about the base of the neck through a 50∘ angle, a motion that lasts 220 ms. The distance from the base of the neck to the center of the head is typically about 20 cm, and the head normally comprises about 6.0% of body weight. Model the motion of the head as having a uniform speed over the course of its pivot. Compute answers to two significant figures.1. What is the acceleration centacent of the head during the collision?2. What force F does the neck exert on the head of a 65 kg65 kg person in the collision? Neglect the force of gravity on the head, and report the answer in units of both newtons and pounds.3. Would headrests mounted to the backs of the car seats help protect against whiplash? Why or why not?a. Yes. A headrest applies an upward force on the head, along the direction of the neck, that cancels the downward force applied by the neck. b. Yes. A headrest ensures that both the head and the body experience the same forward force at roughly the same time. c. No. A headrest applies a mostly horizontal force to the head, so does not affect the mostly vertical force applied by the neck during whiplash. d. No. A headrest reduces the angle traversed by the head, not the speed of the head relative to the body, thus it does not affect the force that the neck applies to the head.

a) a= 19 m/s2, b ) F = F = 38 N

c)  the correct one is B

Explanation:

1) To solve this exercise, let's use the concept of torque, let's start by looking for the mass of the mass of the head, which is 65 of 65 kg

         m= 0.06  65 = 3.9 kg

torque is defined

        τ = F x R

the bold indicate vectors

        τ = F R sin θ

the force is the weight of the head and the distance R = 0.20 m

        τ = mg R sin θ

        τ = 3.9 9.8 0.2 sin 50

        τ = 5.86 N m

Newton's second law expression for rotational motion is

         τ = I α

In general, the head is approximated by a sphere, so the moment of foolishness with respect to the base of the neck (turning point) using the parallel axis theorem is

         I = I_sphere + m d²

Neck height data is not indicated, so we will assume that it is zero (d = 0)

         I = 2/5 m R²

angular and linear acceleration are related

        a = α R

        α = a / R

let's replace

         τ = 2/5 mR²  (a / R)

        a = 5/2 τ / mR

let's calculate

         a = 5/2 5.86 / (3.9 0.2)

         a = 18.8 m / s²

         a= 19 m/s²

2) as the neck and the head are related, the forces are action and reaction, therefore the neck force is

         F = m g

         F = 3.9 9.8 = 38.2 N

          F = 38 N

3) He asks us about the efficiency of the headrest, after reviewing the different alternatives, the correct one is B

Yes. A headrest ensures that both the head and the body experience the same forward force at approximately the same time.

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