Question(I) How much work is done by the gravitational force when a $280-\mathrm{kg}$ pile driver falls 3.80 m ?

Studdy Solution

STEP 1

1. The pile driver has a mass of $280 \, \text{kg}$ .
2. It falls a vertical distance of $3.80 \, \text{m}$ .
3. The acceleration due to gravity is $9.81 \, \text{m/s}^2$ .

STEP 2

1. Recall the formula for work done by a force.
2. Identify the gravitational force acting on the pile driver.
3. Substitute the known values into the formula.
4. Calculate the work done.

STEP 3

Recall the formula for work done by a force:
$W = F \times d \times \cos(\theta)$
where $W$ is the work done, $F$ is the force, $d$ is the distance, and $\theta$ is the angle between the force and the direction of motion.

STEP 4

Identify the gravitational force acting on the pile driver. The gravitational force $F$ is given by:
$F = m \times g$
where $m = 280 \, \text{kg}$ is the mass and $g = 9.81 \, \text{m/s}^2$ is the acceleration due to gravity.

STEP 5

Substitute the known values into the formula for work. Since the force of gravity acts downward and the pile driver falls downward, $\theta = 0^\circ$ and $\cos(0^\circ) = 1$ :
$W = m \times g \times d \times \cos(0^\circ)$ $= 280 \, \text{kg} \times 9.81 \, \text{m/s}^2 \times 3.80 \, \text{m} \times 1$

STEP 6

Calculate the work done:
$W = 280 \times 9.81 \times 3.80$ $= 10431.12 \, \text{J}$
The work done by the gravitational force is:
$\boxed{10431.12 \, \text{J}}$

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