Question

A 36.0-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 416 N. (a) Find the child's speed at the lowest point. (No Response) m/s (b) Find the force exerted by the seat on the child at the lowest point. (Ignore the mass of the seat.

Answer 1

Answer:

a) 6.25 m/s

b) f = 832 N

Explanation:

given data:

mass of child = 36 kg

length 2.94 m

tension  = 416 N

For part (A), we need to add the forces in normal direction F(n),

$F(n) = 2\times T - m\times g = m\times a$

where T is tension

m is mass, g = 9.81 m/s^2, and

a is acceleration is given as.

$a = \frac{v^2}{r}$

where v is speed

r is the radius.  

$2\times T - m\times g = m\times \frac{v^2}{r}$

 $2*(416) - (36)\times (9.81) = (36)* \frac{v^2}{2.94}$

v = 6.25m/s  

Part B)

F = 2*(416)  

F = 832 N  

Answer 2

Answer:v=6.25 m/s

Explanation:

Given

mass of child $m=36 kg$

Length of chain $L=2.94 m$

Tension in each chain $T=416 N$

according to figure

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

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

$\frac{36\times v^2}{2.94}=2\times 416-36\times 9.8$

$v^2=\frac{479.2\times 2.94}{36}$

$v=\sqrt{39.134}$

$v=6.25 m/s$

Force exerted by the seat will be equal to the tension forces i.e. 2T

Force exerted by seat$=2\times 416=832 N$