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Why It’s Innovative: While at first glance this bridge appears to have a straightforward design, the Neal Bridge is unique because it is supported by a series of 23 arches made from fiber-reinforced plastics that are filled with concrete. “There’s been really no new bridge material since high-strength steel and high-strength concrete came in, which was 40 or 50 years ago," MacDonald says. And though the price of composite materials is high, proponents argue that there are significant savings on shipping, construction and long-term maintenance that offset the initial investment. Why It’s Innovative: Pedestrian bridges allow for a certain amount of creativity that’s not possible with structures that need to support heavy-duty use. The undulating outer shell of the Henderson Waves is striking, and the inside is shaped into benches where tourists can sit and gaze at nature or the nearby skyline of Singapore City. The bridge, which is about 900 feet long, is illuminated by an array of LED lights each night to bolster its snake-like presence in the midst of two national parks. Why It’s Innovative: As its name implies, the bridge’s 217-foot-tall support tower acts as a giant sundial. The deck of this pedestrian bridge is made from nonskid glass panels to give walkers a greater sense of the river. MacDonald notes that the deck’s truss bears the bulk of the bridge’s load, while the cables appear slack compared with those of other bridges. Why It’s Innovative: The 32-foot bamboo bridge has a load capacity of 8 tons (though it may actually be able to carry a heavier load), making this one of the first bamboo structures capable of handling trucks. Using lightweight prefabricated materials allowed construction workers to avoid using heavy construction equipment, and the bridge took only a week to install. Why It’s Innovative: With its apex at 1125 feet, the Millau Viaduct is one of the world’s tallest bridges. Despite its huge size, the construction period lasted only three years thanks to the use of GPS guidance systems, self-climbing formwork and prefabricated materials. “What is unusual is to have the towers taper in both directions as they rise," Macdonald says. Why It’s Innovative: Instead of separating in the middle like a drawbridge, the Pont Gustave-Flaubert’s deck is lifted straight up by a butterfly-shaped pulley system so tall ships can pass through. The deck takes about 12 minutes to be pulled all the way up, which happens about 30 or 40 times per year. MacDonald tells PM that using twin roadways allows more sunlight to penetrate the water under the bridge, an important consideration for the river’s ecosystem. Why It’s Innovative: At 22 miles long, the Hangzhou Bay Bridge is the longest ocean-crossing bridge in the world. Engineers had to account for how Hangzhou Bay’s extremely strong tides and powerful typhoons would affect the structure. From end to end, the bridge is slightly S-shaped, which helps it withstand the elements. Future plans include building a service area right in the middle of the bridge. Why It’s Innovative: For centuries it was thought that Da Vinci’s sketch of the bridge was implausible. The bowed arches of the single-span design are dramatically thin where they connect with the walkway, but they flare out as they approach the ground. Da Vinci’s original plan called for the span to be 720 feet long, but Sand and colleagues scaled it down to 300 feet and built the walkway from Norwegian pine. Why It’s Innovative: The sinuous Pythonbrug is one of the most modern bridges in Amsterdam, a city famous for its traditional canal bridges. Unlike Singapore’s Henderson Waves, which relies on an outer shell to create the wave illusion, the Pythonbrug walkway actually dips and rises. While the bridge is certainly an eye-catcher, MacDonald points out that its steep incline wouldn’t pass muster under the Americans With Disabilities Act, which sets a 5 percent limit on the grade of such structures. Why It’s Innovative: A system of six hydraulic rams can pivot the bridge’s walkway at a 40-degree angle in order to let boats pass. Wilkinson Eyre describes the bridge’s movement as looking like a “slowly opening eyelid" when it raises, a process that takes fewer than 5 minutes. Perhaps even more impressive is the fact that the bridge was fully constructed before being installed as a single piece by Europe’s largest floating crane, Asian Hercules II. Why It’s Innovative: The Oresund Bridge is an incredibly complex structure that begins as a cable-stayed bridge in Sweden and ends as a tunnel in Denmark. A small artificial island was built around the tunnel’s entrance to keep water from creeping in. Not only is the bridge equipped to handle four lanes of traffic; it also has a double-track railway. Creating the tunnel was likely the best and cheapest solution to completing the crossing without impeding boat traffic, MacDonald says. Why It’s Innovative: The portion of the bridge’s deck that is supported by the inclined pylon can rotate a full 90 degrees to accommodate passing ships. “A lot of bridge architects, like myself, are trying to get movement into these bridges, and this is one way to do it," MacDonald says. “[Calatrava] is continually trying to put movement in his architecture. You could say he has introduced movement to the built environment, in both buildings and bridges." Why It’s Innovative: Because Lake Washington can be more than 200 feet deep, building a suspension bridge across it was not a viable option in the 1960s. The floating design, which relies on concrete pontoons that are anchored by underwater weights, was the perfect solution. In its more than 40 years of existence, the Evergreen Point Floating Bridge has been battered by high-speed winds and even withstood a barge crashing into it. However, these abuses, along with the bridge’s vulnerability to earthquakes, have forced the Washington Department of Transportation to launch a project aimed at replacing the structure. Why It’s Innovative: The most noticeable attribute of the bridge is how its two levels of traffic cross one another as they pass through the pylon. A series of 144 steel cables were used to support the structure. Brazil spared no expense on this masterpiece; Philips was contracted to develop an energy-efficient system of LED lights that showers the bridge in changing colors and patterns, which the company says consumes 53 percent less energy compared to lighting on other bridges.

Two masses m1 and m2 (with m2 > m1) are connected by a massless rope hung over a frictionless light pulley?

Two masses m1 and m2 (with m2 > m1) are connected by a massless rope hung over a frictionless light pulley. If the masses are released then the acceleration of m2 in the downward direction is given by what equation?

I know that:
Fx: T-m1g=m1a and Fy: T-m2g=-m2a

Please show me how to derive the acceleration of m2 from this.


You have two equations in two unknowns: T (the tension on the rope) and a (the acceleration of both masses - since they are connected, they can't accelerate separately)

From the first equation:

T = m1(a + g)

From the second equation:

m1 (a + g) - m2 g = - m2 a so
m1 a + m1 g - m2g = -m2 a so
(m1 + m2) a = (m2 - m1) g

So: a = g (m2 - m1) / (m2 + m1)

3ds max pulley

Simple pulley rendered with advanced lighting and rope physics.

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