The \"Giant Swing\" at a county fair consists of a vertical central shaft with a

Question

The "Giant Swing" at a county fair consists of a vertical central shaft with a number of horizontal arms attached at its upper end. (See the figure below (Figure 1) ) Each arm supports a seat suspended from a 5.00m -long cable, the upper end of which is fastened to the arm. Take R = 2.20m .

Part A

Find the time of one revolution of the swing if the cable supporting the seat makes an angle of  ? = 40.0? with the vertical.

Part B

Does the angle depend on the weight of the passenger for a given rate of revolution? Yes or No

Explanation / Answer

You have to find the radius of the circular motion. The radius is the distance from the person to the point rotation.

Radius,r = 5 sin40 + 2.20m = 5.414 m

The centripetal force is actually caused by the horizontal tension in the 5.00m cable.

Centripetal force,F = T sin 40
(mv^2) / r = T sin 40 -------------(1)
where,
m = mass of person + seat
v = tangential velocity
r = radius

The weight of the person and seat are balanced by the vertical tension in the 5.00m cable.

mg = T cos 40 ----------------(2)

Combine both equation (1) / (2),

tan 40 = v^2 / rg
v^2 = rg tan40 = 44.52
v = 6.67m/s

v = rW , where W is the angular velocity
6.67 = (5.414)(W)
W = 1.23rad/s

2(pi)(f) = W, where f is the frequency
f = 0.196

1/T = f , where T is the period.
T = 1/f = 5.1s

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.