Question

with the pulleys slider set at 1, predict the minimum force needed to hoist the load. you may want to pay attention to the provided force diagram the size of the upward force compared to the downward force. view available hint(s) slightly greater than 0 n 50 n 125 n slightly greater than 250 n 300 n submit part b how does the minimum force needed to hoist a load change as you increase the number of pulleys from one to two, then three, then four? view available hint(s) the minimum force needed to hoist the load becomes half, then one - third, then one - fourth. the minimum force needed to hoist the load does not change. the minimum force needed to hoist the load becomes double, then three times, then four times. submit

Explanation:

Part A

Step1: Understand pulley mechanics (1 pulley)

With 1 pulley (fixed or single movable, but when "Pulleys" slider is 1, assuming a system where to lift a load, the force needed should counteract the load's weight, but also account for any minimal friction. If the load is, say, 250 N (common context for such problems), with 1 pulley (no mechanical advantage from multiple pulleys), the force needed is slightly more than the load's weight to overcome friction, so slightly greater than 250 N.

Step2: Evaluate options

• "slightly greater than 0 N": Impossible, as load has weight.
• "50 N", "125 N": Too low for 1 pulley (no MA to reduce force much).
• "slightly greater than 250 N": Matches the need to overcome load + friction.
• "300 N": Too high if load is ~250 N, "slightly greater" is more accurate.

Step1: Recall pulley mechanical advantage

Each additional pulley (in a block - and - tackle system) increases the number of supporting ropes, reducing the force needed. For \(n\) supporting ropes, force \(F=\frac{Load}{n}\). With 1 pulley, \(n = 1\) (force ~ load). With 2 pulleys, \(n = 2\) (force ~ load/2), 3 pulleys \(n = 3\) (force ~ load/3), 4 pulleys \(n = 4\) (force ~ load/4).

Step2: Evaluate options

• "The minimum force... half, then one - third, then one - fourth": Matches the mechanical advantage principle (force is inversely proportional to the number of supporting ropes, which increases with each pulley).
• "The minimum force... does not change": Incorrect, as pulleys provide mechanical advantage.
• "The minimum force... double, then three times, then four times": Incorrect, force should decrease, not increase.

Answer:

slightly greater than 250 N

Part B