Question

A waste management company handles large dumpsters of construction debris. The sorting process starts by downloading the dumpster from the transport truck and then dumping its contents into a large hopper as shown below. The waste management plant uses a hydraulic cylinder arrangement to tilt the dumpster to the point that the force of gravity will empty the contents. The plant operator activates an electric pump that pumps hydraulic oil into the input piston at an absolute pressure of 3.50 106 Pa and drives the output plunger, which has a radius of 0.110 m. If the design of the dumping arrangement is such that the output plunger remains perpendicular to the floor of the dumpster, determine the torque the plunger creates about an axis at the end of the dumpster.

Answer 1

what is the distance from output plunger to the end of dumpster ????? please see the figure ( you have not provided the figure) . Some distance must be given in the figure................

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we know

torque = force * lever arm

and

force = pressure * area

here, pressure will be gauge pressure

gauge pressure = absolute pressure - atmospheric pressure

so,

torque = (P - P_atm ) * * r² * d

torque = ( 3.50e6 - 1.013e5) * * 0.11² * d

torque = 129195.7 * d

just multiply the given distance in the diagram and you have the answer. Let me know if you have any doubt.

Thank you.