Final answer:
To calculate the distance the effort must move with a mechanical advantage of 6.0 and 100% efficiency, where the resistance is lifted 2.0 inches, the effort must move a distance of 6 times the resistance distance, resulting in 12 inches.
Step-by-step explanation:
The student is asking about the efficiency of a lever and how to calculate the distance that the effort must move given the mechanical advantage of the lever and the distance that the resistance will be lifted. The mechanical advantage (MA) of a lever is defined as the ratio of the effort arm length to the resistance arm length or alternatively the ratio of resistance force to effort force. In this problem, the given mechanical advantage is 6.0, implying that the effort arm is 6 times longer than the resistance arm or that the effort force is 1/6th of the resistance force. Given the 100% efficiency of the lever, the work done on both sides of the lever will be the same, which means that the product of the effort force and the distance it moves (effort distance, De) will equal the product of the resistance force and the distance it moves (resistance distance).
Solving for De, we see that De will be six times the resistance distance, which is 2.0 inches. Therefore, De = 6.0 * 2.0 inches = 12 inches. The effort must move 12 inches to lift the resistance the required 2.0 inches.