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:v=6.25 m/s

Step-by-step 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=(mv^2)/(L)`

`(mv^2)/(L)=2T-mg`

`(36* v^2)/(2.94)=2* 416-36* 9.8`

`v^2=(479.2* 2.94)/(36)`

`v=√(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* 416=832 N`

Answer 2

a) 6.25 m/s

b) f = 832 N

Step-by-step 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* T - m* g = m* a`

where T is tension

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

a is acceleration is given as.

`a = (v^2)/(r)`

where v is speed

r is the radius.

`2* T - m* g = m* (v^2)/(r)`

`2*(416) - (36)* (9.81) = (36)* (v^2)/(2.94)`

v = 6.25m/s

Part B)

F = 2*(416)

F = 832 N