Question

A 39.0-kg child swings in a swing supported by two chains, each 2.98 m long. The tension in each chain at the lowest point is 416 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

Answer:

a)v=5.81 m/s

b)N= 831.77 N

Explanation:

Given that

m = 39 kg

r= 2.98 m

T= 416 N

a)

Lets take  speed of the boy at the lowest position is v m/s

The radial force Fc

$F_c=\dfrac{mv^2}{r}$

The tension in the chain is T

$2T-mg=\dfrac{mv^2}{r}$

Now by putting the values

$2T-mg=\dfrac{mv^2}{r}$

$2\times 416-39\times 10=\dfrac{39\times v^2}{2.98}$

v²=33.77

v=5.81 m/s

b)

Lets take normal force = N

$N-mg=\dfrac{mv^2}{r}$

Now by putting the values

$N-mg=\dfrac{mv^2}{r}$

$N=mg +\dfrac{mv^2}{r}$

$N=39\times 10+\dfrac{39\times 5.81^2}{2.98}$

N= 831.77 N