Final answer:
To find the distance a 3000 kg pile driver drives a stake into the ground when opposed by a resisting force of 5.0E6 N, we calculate the work done by gravity and set it equal to the work done against the resisting force. Solving for the distance gives us 0.05 meters (Answer A).
Step-by-step explanation:
The problem is a physics question that involves calculating the work done against a resisting force to determine how far a stake is driven into the ground by a pile driver. First, we need to calculate the work done by the gravitational force (also known as potential energy) as the pile driver falls. This is given by the formula Work = mass × gravity × height, which in this case is 3000 kg × 9.8 m/s2 × 8.0 m. Then, we compare this work to the work done against the resisting force, which is calculated by the product of the resisting force and the distance the stake is driven into the ground. Setting them equal, since energy is conserved, and solving for the distance gives us the answer.
To find the distance the stake is driven into the ground on the first stroke, we perform the following steps:
- Calculate the work done by gravity: Workgravity = mass × gravity × height = 3000 kg × 9.8 m/s2 × 8.0 m = 2.35 × 105 joules.
- Set the work done by gravity equal to the work done against the resisting force: Workgravity = Workresisting = Force × distance.
- Solve for the distance: distance = Workgravity / Force = 2.35 × 105 joules / 5.0 × 106 N = 0.047 m, which rounds to 0.05 meters.
Therefore, the correct answer is A. 0.05 meters, which is the distance the stake is driven into the ground on the first stroke.