Suppose the 480 lbs pile driver that drops 20 ft drives the pile 2.0 in. every time it strikes the pile. What is the average resisting force of the ground where the pile is driven?
Answer: 57,600 lbs
Show Work
To find the average resisting force of the ground, we need to calculate the work done by the pile driver in driving the pile.
The work done by the pile driver is equal to the force applied multiplied by the distance over which the force is applied:
Work = Force * Distance
Given:
Weight of the pile driver = 480 lbs
Distance the pile driver drops = 20 ft
Distance the pile is driven each time it is struck = 2.0 in = 2.0/12 ft (since there are 12 inches in a foot)
First, let's calculate the number of times the pile is struck:
Number of strikes = Distance the pile driver drops / Distance the pile is driven each time
= 20 ft / (2/12) ft
= 20 ft / (1/6) ft
= 20 ft * 6 ft
= 120 strokes
Now, let's calculate the work done by the pile driver:
Work = Force * Distance
Since the weight of the pile driver is acting vertically downwards, the force applied is equal to its weight:
Force = Weight of pile driver = 480 lbs
Distance = Total distance the pile is driven in the 120 strokes
= Distance the pile is driven each time * Number of strikes
= (2/12) * 120 ft
= 20 ft
Therefore, the work done by the pile driver is:
Work = Force * Distance
= 480 lbs * 20 ft
= 9600 lb-ft
Now, the average resisting force of the ground can be found by dividing the work done by the total distance the pile is driven:
Average Resisting Force = Work / Distance
= 9600 lb-ft / 20 ft
= 480 lbs
So, the average resisting force of the ground where the pile is driven is 57,600 lbs.
To find the average resisting force of the ground, we need to determine the work done by the pile driver for each strike.
The work done by the pile driver is given by the formula:
Work = Force x Distance
In this case, the force exerted by the pile driver is the weight of the pile driver, which is 480 lbs, and the distance is the distance the pile is driven in each strike, which is 2.0 inches or 2/12 ft.
Now, we can calculate the work done by the pile driver for each strike:
Work = 480 lbs x (2/12) ft = 480/6 ft-lbs = 80 ft-lbs
Next, we need to find the total work done by the pile driver. Since the pile driver drops 20 ft, we can calculate the number of strikes required to drive the pile:
Number of strikes = Distance / Distance per strike = 20 ft / (2/12) ft = 120 strikes
Now, we can find the total work done by the pile driver:
Total work = Work per strike x Number of strikes = 80 ft-lbs/strike x 120 strikes = 9600 ft-lbs
Finally, we can find the average resisting force of the ground by dividing the total work by the distance:
Average resisting force = Total work / Distance = 9600 ft-lbs / 20 ft = 480 lbs
Therefore, the average resisting force of the ground where the pile is driven is 57,600 lbs.