# What is the magnitude of the upward force exerted by the chain on the boulder as it rises out of the quarry? (include units with answer)?

A 630 kg boulder is raised from a quarry 125 m deep by a long uniform chain that has a mass of 492 kg. This chain is of uniform strength, but at any point, it can support a maximum tension no greater than 3.50 times its weight without breaking. What is the magnitude of the upward force exerted by the chain on the boulder as it rises out of the quarry? (include units with answer) The correct answer is NONE of the following: 663.69 N, 16875.6 N, 6180.3 N, 3304.98 N, 16881.6 N, and 3087 N. The maximum constant acceleration the boulder can have and still get out of the quarry is 5.246 m/s^2.

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• At the TOP of the chain, the required force with zero acceleration is

F = (492 + 630)kg * 9.8m/s² = 10 996 N

which ought to be rounded to 11 000 N, IMO, owing to the data.

Your last statement doesn't seem to be related to anything else in the problem statement. Maybe you're to show that the maximum acceleration is 5.246 m/s².

Maximum tension

T = 3.50 * 492kg * 9.8m/s² = 16 875.6 N

force at top of chain required for acceleration "a" is

F = (492 + 630)kg * (9.8m/s² + a)

equating these

16 875.6 N = 1122kg * (9.8m/s² + a)

which solves to

a = 5.241 m/s²

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