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Jais Flight is the longest zipline in the world. Soar across jagged mountain peaks and swoop through deep ravines at hair-raising speeds of up to 160 kmph. Three minutes of adrenaline-pumping adventure at 1680 metres above the Arabian Gulf will leave you with a once-in-a-lifetime sense of superhero magic.
Forces Action on Rider:
Forces Action on Rider:
A person, mass M, is riding a zipline from a platform D meters above the ground to a platform A above the ground. The velocity of the person at platform D is v0 The zipline is inclined at an angle of θ to the horizontal, and the total length of the cable is L m. The zipline experiences a constant kinetic friction force of R due to the pulley system and air resistance. The zipline is designed so that the rider arrives at platform A with a velocity of v.
On the diagram above, label the following measurements: M, D, A, v0, L, v
At the position shown, on the dot shown below, draw a labeled free-body diagram for the person on the zipline while in motion, all forces should start on the dot..
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Write the equation for the net force acting along the zipline in terms of m, g, Ff, and θ, and any other variables as necessary.
Sagging Cable:
Sagging Cable:
The zipline cable sags due to its own weight, causing the angle of the cable (θ) to vary as the rider moves along the length of the cable. At the midpoint of the cable, the sag is most pronounced, and the angle is smallest. As the rider moves closer to the bottom platform, the angle increases again. The diagram below shows an exaggerated view of the cable between the towers.
Explain how the rider's velocity changes as they move along the sagging cable. Consider the varying angle of inclination (θ) and the forces acting on the rider.
Using energy principles, derive an equation for the rider’s velocity v(x) at any point x along the zipline, assuming the height h(x) and distance traveled d(x) are known.
Derive an expression for the acceleration at any point along the cable. Express it in terms of m, g, Ff, and θ.
Assuming no friction, in terms of m, g, θ, and any other variables necessary, express the theoretical speed (v) of the person when they reach the bottom platform (A), using conservation of energy principles.
Body Postion and Speed:
Body Postion and Speed:
The graph above shows the speed of a rider in the Cannonball Body Position.
Based on the graph, explain how the shape of the velocity-time graph reflects the changing acceleration of the rider. Relate your explanation to the varying angle (θ) and the forces acting on the rider.
On the graph above, sketch an additional line to represent a person that chooses to ride in the Starfish Body Position during the ride.
Justify the shape of your sketched line.
Specific Scenario:
Specific Scenario:
The following values are given for a specific scenario: A 75 kg person is riding a zipline from a platform 15 m above the ground to a platform 5 m above the ground. The zipline is straight (taut) and inclined at an angle of 15° to the horizontal, and the total length of the cable is 50 m. The zipline experiences a constant kinetic friction force of 50 N due to the pulley system and air resistance.
Calculate the work done by the frictional force over the entire length of the zipline.
How does the work done by friction affect the person’s final speed? Use the work-energy principle to determine their actual speed at the bottom platform.
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