BIO Head injuries in sports A research group at Dartmouth College has developed a Head Impact Telemetry (HIT) System that can be used to collect data about head accelerations during impacts on the playing field. The researchers observed 249,613 impacts from 423 football players at nine colleges and high schools and collected collision data from participants in other sports. The accelerations during most head impacts (>89%) in helmeted sports caused head accelerations less than a magnitude of 400 m/s 2 . However, a total of 11 concussions were diagnosed in players whose impacts caused accelerations between 600 and 1800 m/s 2 , with most of the 11 over 1000 m/s 2 . Use Eq. (2.7) and the numbers from Problem 86 to determine which stopping distance is closest to that which would lead to a 1000 m/s 2 head acceleration. a. 0.005 m b. 0.5 m c. 0.1 m d. 0.01 m e. 0.05 m
BIO Head injuries in sports A research group at Dartmouth College has developed a Head Impact Telemetry (HIT) System that can be used to collect data about head accelerations during impacts on the playing field. The researchers observed 249,613 impacts from 423 football players at nine colleges and high schools and collected collision data from participants in other sports. The accelerations during most head impacts (>89%) in helmeted sports caused head accelerations less than a magnitude of 400 m/s 2 . However, a total of 11 concussions were diagnosed in players whose impacts caused accelerations between 600 and 1800 m/s 2 , with most of the 11 over 1000 m/s 2 . Use Eq. (2.7) and the numbers from Problem 86 to determine which stopping distance is closest to that which would lead to a 1000 m/s 2 head acceleration. a. 0.005 m b. 0.5 m c. 0.1 m d. 0.01 m e. 0.05 m
BIO Head injuries in sports A research group at Dartmouth College has developed a Head Impact Telemetry (HIT) System that can be used to collect data about head accelerations during impacts on the playing field. The researchers observed 249,613 impacts from 423 football players at nine colleges and high schools and collected collision data from participants in other sports. The accelerations during most head impacts (>89%) in helmeted sports caused head accelerations less than a magnitude of 400 m/s2. However, a total of 11 concussions were diagnosed in players whose impacts caused accelerations between 600 and 1800 m/s2, with most of the 11 over 1000 m/s2.
Use Eq. (2.7) and the numbers from Problem 86 to determine which stopping distance is closest to that which would lead to a 1000 m/s2 head acceleration.
64. Two springs have the same unstretched length but different spring
constants, k₁ and k₂. (a) If they're connected side by side and
stretched a distance x, as shown in Fig. 4.24a, show that the force
exerted by the combination is (k₁ + k₂)x. (b) If they're con-
nected end to end (Fig. 4.24b) and the combination is stretched a
distance x, show that they exert a force k₁k2x/(k₁ + k₂).
www
(a)
FIGURE 4.24 Problem 65
www
(b)
65. Although we usually write Newton's second law for one-dimensional
motion in the form F =ma, which holds when mass is constant,
d(mv)
a more fundamental version is F
=
.
Consider an object
dt
whose mass is changing, and use the product rule for derivatives to
show that Newton's law then takes the form F
dm
= ma + v
dt
If a proton is located on the x-axis in some coordinate system at x0 = -3.2 x 10-5 meters, what is the x-component of the Electric Field due to this proton at a position x = +3.2 x 10-5 meters and on the x axis as the y-axis is 0 giving a number of Newtons/Coulomb?
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