the hammer of a pile driver weighs 3800N and must be lifted vertically 2.80 m at constant speed in 4.00 s . What horsepower must the engine provide to the hammer?
Isn't power= work/time ?
To determine the horsepower required to lift the hammer, we can use the formula:
Horsepower = (Work / Time) / 746
First, let's calculate the work done to lift the hammer:
Work = Force x Distance
Given that the force (weight of the hammer) is 3800 N and the distance is 2.80 m, we have:
Work = 3800 N x 2.80 m = 10,640 N•m
Next, we need to find the time taken for the lifting:
Time = 4.00 s
Now, let's substitute the values into the formula to find the horsepower:
Horsepower = (10,640 N•m / 4.00 s) / 746
Horsepower = 2,660 N•m/s / 746
Horsepower ≈ 3.57 hp
Therefore, the engine must provide approximately 3.57 horsepower to lift the hammer.
To find the horsepower required by the engine to lift the hammer, we need to apply the formula:
Horsepower = Work / Time
First, let's calculate the work done in lifting the hammer. The work is given by the product of force and distance:
Work = Force * Distance
In this case, the force is equal to the weight of the hammer, which is given as 3800N. The distance is given as 2.80m. Therefore:
Work = 3800N * 2.80m
Next, divide by time to get the power:
Power = Work / Time
In this case, the time is given as 4.00s. Therefore:
Power = (3800N * 2.80m) / 4.00s
Now, let's solve for the power in watts:
Power = (3800N * 2.80m) / 4.00s
Power = 26600Nm / 4.00s
Power = 6650 Watts
Finally, to convert watts to horsepower, we divide by 746 (since 1 horsepower is equal to 746 watts):
Horsepower = 6650 Watts / 746
Horsepower ≈ 8.91 horsepower
Therefore, the engine must provide approximately 8.91 horsepower to lift the hammer.