A 43.0-kg child swings in a swing supported by two chains, each 2.94 m long. The tension in each chain at the lowest point is 340 N. (a) Find the child's speed at the lowest point. m/s (b) Find the force exerted by the seat on the child at the lowest point. (Ignore the mass of the seat.) N (upward)

a) 4.2 m/s

b) 680 N

Explanation:

Given that

Mass of the child, m = 43 kg

Length of the chain, r = 2.94 m

Tension in the chain, T = 340 N

Then...

a) F(net) = mv²/r + mg

340 * 2 = (43 * v²)/2.94 + 43 * 9.8

680 = 43v² / 2.94 + 421.4

43v² / 2.94 = 680 - 421.4

43v² / 2.94 = 258.6

43v² = 258.6 * 2.94

43v² = 760.284

v² = 760.284 / 43

v² = 17.68

v = √17.68

v = 4.2 m/s

(b) 680 N

Conclusively, the child's speed at lowest point is 4.2 m/s

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