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.
The work done is given by the formula:
Work = Force * Distance
In this case, the distance is the total distance the pile is driven, which is given as 20 ft. The force is the weight of the pile driver, which is given as 480 lbs.
Now we need to calculate the number of times the pile is struck. Each strike drives the pile by 2.0 in, which is equivalent to 2.0 / 12 = 0.167 ft.
The number of strikes is then calculated as:
Number of strikes = Total distance / Distance per strike
= 20 ft / 0.167 ft
= 119.76 strikes
Since we cannot have fractional strikes, we round this down to 119 strikes.
Now we can find the total work done:
Total work = Work per strike * Number of strikes
= Force * Distance per strike * Number of strikes
= 480 lbs * 0.167 ft * 119 strikes
= 9528.96 lb-ft
Finally, to find the average resisting force, we need to divide the total work by the total distance:
Average resisting force = Total work / Total distance
= 9528.96 lb-ft / 20 ft
= 476.448 lb
Rounding this to the nearest hundredth, we find that the average resisting force of the ground is approximately 476.45 lb.
To find the average resisting force of the ground, we need to calculate the work done by the pile driver's impact on the pile.
The work done is equal to the force applied multiplied by the distance moved. In this case, the force applied is the weight of the pile driver, which is 480 lbs, and the distance moved is the height the pile is driven each time, which is 2.0 in.
First, let's convert the height from inches to feet:
2.0 in = 2.0/12 = 0.17 ft
Now we can calculate the work done for each strike:
Work = force * distance
Work = 480 lbs * 0.17 ft
Work = 81.6 ft-lbs
Next, let's find the total work done by summing up the work done for each strike. But before that, we need to know the total number of strikes. Since the height of the pile is reduced by 2.0 inches with each strike, we can calculate the number of strikes using the height of the pile before driving:
Total height of pile = 20 ft
Height reduced per strike = 2.0 in = 2.0/12 = 0.17 ft
Number of strikes = Total height of pile / Height reduced per strike
Number of strikes = 20 ft / 0.17 ft
Number of strikes = 117.6 (approx.)
As the number of strikes is not a whole number, we need to round it to the nearest whole number. Hence, there will be 118 strikes.
Now let's calculate the total work done:
Total work = work per strike * number of strikes
Total work = 81.6 ft-lbs * 118
Total work = 9628.8 ft-lbs
Finally, to find the average resisting force, we divide the total work by the total distance the pile is driven:
Average resisting force = Total work / Total distance
Average resisting force = 9628.8 ft-lbs / 20 ft
Average resisting force = 481.44 lbs
Therefore, the average resisting force of the ground where the pile is driven is approximately 57,600 lbs.