Final answer:
The work done to raise a 300 lb. box 1 foot using a ten-foot beam is 405.7 J. The mechanical advantage when the box sits 3 feet from the fulcrum is 3. The smallest amount of force needed to lift the box 1 foot is 444.8 N.
Step-by-step explanation:
To calculate the work done to raise a 300 lb. box 1 foot using a ten-foot beam, we can use the formula W = fd, where W is the work done, f is the force applied, and d is the distance moved. First, we need to convert the weight of the box from pounds to newtons. 1 lb is approximately equal to 4.448 N, so 300 lb is equal to 1334.4 N. The distance moved is 1 foot, which is approximately 0.3048 meters. Plugging these values into the formula, we get W = 1334.4 N * 0.3048 m = 405.7 J.
If the box sits 3 feet from the fulcrum, the mechanical advantage can be calculated using the formula MA = d1 / d2, where d1 is the distance from the fulcrum to the applied force and d2 is the distance from the fulcrum to the load. In this case, d1 is 3 feet and d2 is 1 foot. Plugging these values into the formula, we get MA = 3 / 1 = 3.
To find the smallest amount of force needed to lift the box 1 foot, we can use the formula F = W / MA, where F is the force needed, W is the weight of the box, and MA is the mechanical advantage. In this case, W is 1334.4 N and MA is 3. Plugging these values into the formula, we get F = 1334.4 N / 3 = 444.8 N.