Answer to Question #247503 in Molecular Physics | Thermodynamics for Anuj

Question

A 38.0-kg child swings in a swing supported by two chains, each 2.90 m long. The tension in each chain at the lowest point is 436 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)

Answer 1

m=38.0 kg

l=2.90 m

T=436 N

(a) Child perform circular motion, so centripetal force acts on child

Force body diagram:

Centripetal force acts along the length of chain towards the support.

According to Newton's second law,

$F_{net} = centripetal \; force = \frac{mv^2}{r} \\ T+T-mg=\frac{mv^2}{r} \\ 2T-mg = \frac{mv^2}{r} \\ v^2 = \frac{r(2T-mg)}{m}$

r = radius of the circular path = length of chain = 2.90 m

$v^2 = \frac{2.90(2 \times 436-38 \times 9.81}{38} \\ v^2= 38.098 \\ v=6.17 \;m/s$

(b)

$N’ -mg = \frac{mv^2}{r} \\ 2T-mg = \frac{mv^2}{r} \\ 2T=N’ \\ N’ = 2 \times 436 = 872 \;N$

The force exerted by the seat on the child at the lowest point is 872 N.