**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 ๐ = 5000 ๐๐ and the distance ๐ฅ = 20 m

When ๐ = 5000 kg, find and plot the moment at O as a function of ๐ฅ, and determine the value of ๐ฅ when the moment at O is zero

If the magnitude of the maximum moment at O is 2,500 kNโm 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 ๐คโ = 0.7 m, ๐คโ = 1.4 m, ๐ = 1000 ร (5 โ 0.010 ร ๐) ๐๐, 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 ๐กโ and ๐กโ in m/s, km/h, and mph. Individual ๐กโ and ๐กโ 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 ๐ก = 62 (๐ ) 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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