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.