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Lifting a Boulder from a quarry with constant acceleration

A 730-kg boulder is raised from a quarry 123 m deep by a long uniform chain having a mass of 560 kg . This chain is of uniform strength, but at any point it can support a maximum tension no greater than 3.00 times its weight without breaking.

A) What is the maximum acceleration the boulder can have and still get out of the quarry?

B) How long does it take to be lifted out at maximum acceleration if it started from rest?

Solution Preview

See attached file.

Mass of chain M(C) = 560 Kg

Weight of chain therefore produces force F(C) where F(C) = M(C)*g (1)

Mass of Boulder M(B) = 730 Kg

Weight of chain therefore produces force F(B) where F(B) = M(B)*g (2)

Let the Tension in cable be T

Where we are told that T < 3*F(C) before the chain breaks

Equating forces we can say that the net force upwards (F(net)) on the Boulder can be given by (3)

F(net) = T - M(C)*g - ...

Solution Summary

This problem/solution looks at investigating the raising of a boulder of known mass from a Quarry using a metal link chain. The maximum breaking tension in the chain is given as 3x the weight of the boulder. One is asked to deduce the maximum acceleration that can be given to the pulling process to lift the Boulder from the Quarry without the chain breaking. Linear kinematics is then applied under maximum acceleration conditions to deduce the minimum time taken to lift the boulder from the Quarry of known depth with the boulder starting from rest.