Question

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)

Answer 1

Answer:695.5 N

Explanation:

mass of child $m=41 kg$

Length of chain $L=2.98 m$

Tension in each chain $T=348 N$

(a)Tension at bottom point $T=348 N$

At lowest Point

$T+T-mg=\frac{mv^2}{L}$

$2T-mg=\frac{mv^2}{L}$

$2\times 348-41\times 9.8=\frac{41\times v^2}{2.98}$

$v^2=\frac{294.2\times 2.98}{41}$

$v=\sqrt{21.38}=4.62 m/s$

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

$N-mg=\frac{mv^2}{L}$

$N=mg+\frac{mv^2}{L}$

$N=41\times 9.8+\frac{41\times 21.38}{2.98}$

$N=695.95 N$