Counterweight M x- +3.4 m 7.7 m

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Chapter1: Units, Trigonometry. And Vectors
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A tower crane (Figure 1) must always be carefully balanced so that there is no net torque tending to tip it. A particular crane at a building site is about to lift a m = 2700-kg air-conditioning unit. The crane's dimensions are shown in (Figure 2). The crane's counterweight has a mass of M = 10000 kg . Ignore the mass of the beam.

Where must the crane's counterweight be placed when the load is lifted from the ground? (The counterweight is usually moved automatically via sensors and motors to precisely compensate for the load.)
Express your answer to two significant figures and include the appropriate units.

Determine the maximum load that can be lifted with this counterweight when it is placed at its full extent.
Express your answer to two significant figures and include the appropriate units.

The image depicts two tall construction cranes set against the backdrop of a sunset. The sky features a gradient of colors, transitioning from deep blue at the top to warm orange hues near the horizon, creating a striking silhouette effect for the cranes. Both cranes are tower types, with long horizontal arms used for lifting materials. The cranes are positioned at a construction site, indicated by the presence of partially constructed buildings and several streetlights. The scene captures the architectural and engineering aspects of urban development, showcasing how large-scale construction projects are facilitated by such machinery. This image exemplifies the integration of technology and infrastructure in modern city landscapes.
Transcribed Image Text:The image depicts two tall construction cranes set against the backdrop of a sunset. The sky features a gradient of colors, transitioning from deep blue at the top to warm orange hues near the horizon, creating a striking silhouette effect for the cranes. Both cranes are tower types, with long horizontal arms used for lifting materials. The cranes are positioned at a construction site, indicated by the presence of partially constructed buildings and several streetlights. The scene captures the architectural and engineering aspects of urban development, showcasing how large-scale construction projects are facilitated by such machinery. This image exemplifies the integration of technology and infrastructure in modern city landscapes.
The image illustrates the side view of a crane in operation. The crane consists of a vertical support pillar and a horizontal beam. The horizontal beam extends 7.7 meters from the pillar, where it supports a load denoted by "m". On the opposite side of the vertical pillar, a counterweight labeled "M" is placed. The counterweight is located at a distance "x" from the base of the vertical pillar. Alongside the value "x", there is a solid distance marked as 3.4 meters from the pillar towards the counterweight.

This diagram is an essential component in studying the principles of torque and equilibrium in physics. It demonstrates how cranes maintain balance through appropriate distribution of weight, highlighting the significance of counterweights in stabilizing structures while lifting heavy loads.
Transcribed Image Text:The image illustrates the side view of a crane in operation. The crane consists of a vertical support pillar and a horizontal beam. The horizontal beam extends 7.7 meters from the pillar, where it supports a load denoted by "m". On the opposite side of the vertical pillar, a counterweight labeled "M" is placed. The counterweight is located at a distance "x" from the base of the vertical pillar. Alongside the value "x", there is a solid distance marked as 3.4 meters from the pillar towards the counterweight. This diagram is an essential component in studying the principles of torque and equilibrium in physics. It demonstrates how cranes maintain balance through appropriate distribution of weight, highlighting the significance of counterweights in stabilizing structures while lifting heavy loads.
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