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Value, Direction, and Balancing a Resultant Force

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There are three people pushing on a box, as illustrated. Each of the three forces is 45 degrees from the x and y axes (there is no friction between the box and the floor).

Picture of box is attached. The arrows are NOT to scale.

a. Find the value and direction of the resultant force.
b. What single force could be added to the box by a fourth person, to balance the resultant force?

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Solution Summary

Solution provides equations to find the value and direction of a resultant force, as well as what single force could be added to the box by a fourth person, in order to balance the resultant force. Expert only provides equations.

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Pistons on a refrigeration compressor

A single acting refrigeration reciprocating compressor has six pistons pitched 100mm from each other on the shaft. The pair cranks on VW formation are positioned on 120 degrees apart from each other on the shaft and compression- suction sequence is in the order of 1-6, 2-5, and 3-4. Calculate the out of balance torque when the shaft rotates at 1450rpm if the mass of each piston is 350g. Take the central plane of the shaft as reference.

What is the difference in torque when the compression-suction order is 1-4, 5-2, and 3-6 and explain why removing mass is better than adding a counter balance mass.

Also take crank radius as being 200mm

Show workings and calculations (simple drawing attached)

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