Question

Question 2: #67 In the Pirate Boat ride at the amusement park, riders swing back and forth in a pendulum-like “boat”. The distance from the boat to the pivot is 13 m, and the maximum angle the boat reaches is 40o. What is the maximum speed the boat attains? What is the apparent weight of a 55 kg rider at the bottom of the arc?

Answer 1

given
L = 13 m
theta = 40 degrees
m = 55 kg

maximum height above lowest point,
h_max = L*(1 -cos(theta))

= 13*(1 -cos(40))

= 3.04 m

now apply conservation of energy,

(1/2)*m*v_max^2 = m*g*h_max

v_max = sqrt(2*g*h_max)

= sqrt(2*9.8*3.04)

= 7.72 m/s <<<<<<<<<<<<--------------Answer

apparent weight = m*g + m*a

= m*g + m*v_max^2/L

= 55*9.8 + 55*7.72^2/13

= 791 N <<<<<<<<<<<<--------------Answer