Question

A neighbor's child wants to go to a neighborhood carnival to experience the wild rides. The neighbor is worried about safety as one of the rides looks dangerous. and asks for your advice. the ride in question has a 10-lb chair which hangs freely from a 30-ft long chain attached to a pivot on the top of a tall tower. when a child enters the ride, the chain is hanging straight down. the child is then attached to the chair with a seat belt and shoulder harness.

When the ride starts up the chain rotates about the tower and reaches a maximum speed and remains at thta speed. It rotates the tower once every 3 seconds.

When you ask the operator he says that the ride is safe and sits in a stationary chair which creaks but holds the 200 pounds.

Has the operator shown that the ride is safe for a 50 lb child?

Answer 1

According to the result obtained, the trip is not safe for a 50 lb child.

Step-by-step explanation:

The sum of forces in y must be equal to zero:

∑Fy = 0

0 = W + Tcosθ

The sum of forces in x:

∑Fx = m*a = -m*W²*r = -T1sinθ

r = Lsinθ

m*W²*Lsinθ = T1sinθ

`m(4\pi ^(2)L )/(T^(2) ) =T\\(60)/(32) (4\pi ^(2) 30)/(3^(2) ) =T\\T=250lb`

Like 250 lb > 200 lb, the answer is no

Answer 2

No, the ride is not safe

Step-by-step explanation:

From the diagram attached, it is seen that

`\sum f_(y) = 0`

`\tau cos \theta - W = 0`................(1)

`\sum f_(x) = 0`

`-ma + \tau sin \theta = 0`.......(2)

`a = w^(2) r`

From the diagram,
`r = Lsin \theta`

`a = w^(2) L sin \theta`

`w = (2\pi )/(T)`

`a = (4\pi ^(2)L sin \theta )/(T^(2) )`............(3)

Put (3) into (2)

`\tau sin \theta = (4\pi ^(2)m L sin \theta )/(T^(2) )`

`\tau = (4\pi ^(2)m L )/(T^(2) )`

w = weight of chair + weight of child = 50 + 10 = 60 lb

g = 32 ft/s²

m = w/g = 60/32 = 1.875

L = 30 ft

T = 3 secs

`\tau = (4\pi ^(2)*1.875*30 )/(0.3^(2) )`

`\tau = 246.74 lbs`

since 246.74 lbs > 200 lbs, it is not safe because the stationary chair will creak