A 41.0 kg child swings in a swing supported by two chains, each 2.98 m long. (a) If the tension in each chain at the lowest point is 348 N, find the child's speed at the lowest point. m/s (b) What is the force exerted by the seat on the child at the lowest point? (Neglect the mass of the seat.) N (upward)

Respuesta :

Answer:695.5 N

Explanation:

mass of child [tex]m=41 kg[/tex]

Length of chain [tex]L=2.98 m[/tex]

Tension in each chain [tex]T=348 N[/tex]

(a)Tension at bottom point [tex]T=348 N[/tex]

At lowest Point

[tex]T+T-mg=\frac{mv^2}{L}[/tex]

[tex]2T-mg=\frac{mv^2}{L}[/tex]

[tex]2\times 348-41\times 9.8=\frac{41\times v^2}{2.98}[/tex]

[tex]v^2=\frac{294.2\times 2.98}{41}[/tex]

[tex]v=\sqrt{21.38}=4.62 m/s[/tex]

(b)Force exerted by Seat will be Equal to Normal reaction

[tex]N-mg=\frac{mv^2}{L}[/tex]

[tex]N=mg+\frac{mv^2}{L}[/tex]

[tex]N=41\times 9.8+\frac{41\times 21.38}{2.98}[/tex]

[tex]N=695.95 N[/tex]