While exploring an elaborate tunnel system, you and your team get lost and find yourselves at the bottom of a 450-m vertical shaft. Suspended from a thick rope (near the floor) is a large rectangular bucket that looks like it had been used to transport tools and debris up and down the tunnel. Mounted on the floor near one of the walls is a gasoline engine (3.5 hp) that turns a pulley and rope, and a sign that reads “Emergency Lift.” It is clear that the engine is used to drive the bucket up the shaft. On the wall next to the engine is a sign indicating that a full tank of gas will last exactly 15 minutes when the engine is running at full power. You open the engine’s gas tank and estimate that it is ¼ full, and there are no other sources of gasoline.

(a) Assuming zero friction, if you send your team’s lightest member (who weighs 125 lb), and the bucket weighs 150 lb when empty, how far up the shaft will the engine take her (and the bucket)? Will it get her out of the mine?

(b) Assuming an effective collective friction (from the pulleys, etc.) of ????_eff = 0.10 (so that F_f = ????_eff Mg, where M is the total mass of the bucket plus team member), will the engine (with a ¼-full tank of gas  lift her to the top of the shaft?