Achild lying on her back experiences 52.0 n tension in the muscles on both sides of her neck when she raises her head to look past her toes. later, sliding feet first down a water slide at terminal speed 6.30 m/s and riding high on the outside wall of a horizontal curve of radius 2.40 m, she raises her head again to look forward past her toes. find the tension in the muscles on both sides of her neck while she is sliding.

F = 73.84 N

Explanation:

First the horizontal acceleration due to the circular motion:

a = v^2/r

= (6.30)^2/2.40= 16.54 m/s^2

In her own non-inertial frame, her head feels a horizontally outward fictitious force equal to its  mass times this acceleration.

Together this force and the weight of her head add to have a magnitude equal to the mass of her head times an acceleration of

a = ((g^2+(v^2/4)^2)^(1/2)=

a = (9.8^2 + (6.3^2/4)^2)^1/2 =  13.94 m/s^2.

This is larger than g by a factor of

13.94/9.80= 1.42

Thus, the force required to lift her head is larger by this factor, or the required force is

F = (1.42)*(52.0)= 73.84 N