Respuesta :
Answer:
The total tension in the child's neck muscle, T = 56.51 N
Explanation:
Let m = mass of the child's neck
Radius of the curve, r = 2.40 m
The child's speed, v = 3.35 m/s
The tension force on the child's neck when he raises his head up off the floor, [tex]T_{f} = 51.0 N[/tex]
The tension force on the child's neck when he raises his head from the wall of the slide, [tex]T_{s} = ?[/tex]
[tex]T_{f} = mg\\g = 9.8 m/s^2\\51 = m * 9.8\\m = 51/9.8\\m = 5.2 kg[/tex]
Since he makes a circular turn in water, the radial acceleration can be given by the equation:
[tex]a_{r} = \frac{v^{2} }{r} \\a_{r} = \frac{3.35^{2} }{2.4}\\a_{r} = 4.68 m/s^2[/tex]
[tex]T_{s} = ma_{r} \\T_{s} = 5.2 * 4.68\\T_{s} = 24.336 N[/tex]
The total tension in the child's neck muscle till be calculated as:
[tex]T = \sqrt{T_{f} ^{2} + T_{s} ^{2} } \\T = \sqrt{51 ^{2} + 24.336^{2} }\\T = \sqrt{2601 + 592.24 }\\T = 56.51 N[/tex]
