Final answer:
The total work done by the crane is calculated by adding the work done during each phase of the lifting process, amounting to 500 kJ. To find tension in the cable during another kind of lift, one would apply static equilibrium principles. Historical achievements in lifting machinery, like the Castello, underline the significance of technological advances in construction.
Step-by-step explanation:
Total Work Done by the Crane
To calculate the total work done by the crane when lifting construction materials, we must analyze the different phases of the lifting process. The first phase involves the motor increasing the force from 0 to 10 kN over 10 m. Since this is a linear increase, we can find the average force exerted over this distance, which will be 5 kN. The work done in this phase is the average force multiplied by the distance, giving us 50 kJ (kilojoules). For the second phase, the motor exerts a constant force of 10 kN over 40 m, resulting in 400 kJ of work. In the final phase, the force winds down from 10 kN to 0 N over the last 10 m, which is symmetrical to the first phase and thus has the same amount of work done at 50 kJ. The total work is therefore the sum of these three amounts, which is 50 kJ + 400 kJ + 50 kJ, totaling 500 kJ.
Another scenario involves determining the tension in the cable of a crane lifting a load with a boom. To find the tension in the cable and the force at the axle, one would apply the principles of static equilibrium and consider the torques and forces on the crane's boom and the weights involved, including the load and the boom itself.
Historically, lifting designs like the Castello were crucial in efficient construction, indicating the importance of machinery development in historical construction techniques. These design breakthroughs allowed for more effective handling of materials such as heavy sandstone beams.