Question 1
Figure 1 shows a tower crane with the properties listed in Table 1. The distance between the trolley and mast x can change from 0 to dj (Figures 1 and 2).
Table 1: Specifications of the tower crane
Draw the free body diagram of the tower crane and calculate the reactions at O when the mass of the lifted body 𝑚 = 5000 𝑘𝑔 and the distance 𝑥 = 20 m
When 𝑚 = 5000 kg, find and plot the moment at O as a function of 𝑥, and determine the value of 𝑥 when the moment at O is zero
If the magnitude of the maximum moment at O is 2,500 kN∙m and the magnitude of the maximum force at O is 1,650 KN, calculate the maximum mass of the body that the tower crane can lift regardless of the trolley location.
When lifting heavy bodies with two points is required, a spreader beam is used (Figure 3). If 𝑤₁ = 0.7 m, 𝑤₂ = 1.4 m, 𝑚 = 1000 × (5 − 0.010 × 𝑆) 𝑘𝑔, and the mass of the spreader is negligible:
1. Calculate the tension forces in the slings AB and CD when the lifted body is not tilted
2. To prevent the body from tilting, what should be considered in the design and operation of the spreader beam?
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Figure 1: its model
Figure 2: Tower crane specifications
Question 2
The car acceleration time history for 62 seconds (i.e., between 2:42:27 pm and 2:43:29 pm) is shown in figure 4. During this time, the car accelerates from 36 mph (Miles per hour) to 200 mph and then decelerated to 24 mph. your tasks for this question are,
Calculate the velocity at time 𝑡₁ and 𝑡₂ in m/s, km/h, and mph. Individual 𝑡₁ and 𝑡₂ are provided for each student in the attached file
Bring evidence from the video to show the accuracy of your calculation. For example, the calculated velocity at 𝑡 = 62 (𝑠) is 29.3 mph. The actual velocity based on the following figure is 24 which is close to the calculated velocity
Compare your calculated velocities with the actual velocities of the car and calculate their differences in percent.
Explain the reasons for discrepancies between calculated and actual velocities.
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