(14%) Problem 8: The Slingshot is a ride for two people. It consists of a single
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(14%) Problem 8: The Slingshot is a ride for two people. It consists of a single passenger cage, two towers, and two elastic bands. Potential energy is stored in the elastic bands and the passenger cage is released. On the way up, this potential energy in the elastic bands is converted into the kinetic energy of the cage. At the maximum height potential energy of the cage. The slingshot has two towers of height h-78 m. The towers are a distance d 35 m apart. Each elastic band has an unstretched length of Lo 42 m and a spring constant of k 285 N/m. The total mass of the passengers and cage is m 390 kg. The car is pulled down to the ground in the middle of the two towers. of the ride, the energy has been converted into gravitational 1 ©theexpertta.com 20% Part (a) Write an expression for the stretched length L of one of the elastic bands strung from the cage to the top of its tower Grade Summary Potential Submissions 1/2 o (h2+ d2)12-L0 (h222 (+(d/2)2y1/2 100% Attempts remaining: 5 0% per attempt) detailed view Oh2+(d/2)2 (h2+(d/2)12 Submit Hint I give up! Hints: 0% deduction pe r hint. Hints remaining: 3 Feedback: 0% deduction per feedback. 20% Part (b) Calculate the stretched length, in meters, of each band 20% Part (c) Write an expression for the total potential energy stored in the elastic bands before the cage is released 20% Part (d) Calculate the total potential energy, in joules, stored in the elastic bands before the cage is released 20% Part (e) Calculate the maximum height, in meters, of the rideExplanation / Answer
(a)
From pythagoras theorem,
L2 = h2 + (d/2)2
L = [h2 + (d/2)2] 1/2
(b)
L = [782 + (35 / 2)2] 1/2
L = 79.93 m
(c)
Total Potential energy,
U = 2*[(1/2)kx^2]
where x = L - Lo
U = k*(L - Lo)^2
(d)
U = 285 * (79.93 - 42)^2
U = 41.02*10^4 J
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