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Check your answer by repeating the calculation, using the other way. Do you get the same answer? To find the maximum allowed weight of the unit, define the x axis to be parallel to the roof with upward along the roof positive and downward negative and the y axis to be perpendicular to the roof with away from the roof positive and into its negative.

The magnitude of the normal force N is acting in the positive y direction. Here, is the angle between the roof with the x axis and is the weight of the air-conditioning unit. From the above figure, the normal force is equal to the magnitude of the weight w acting in the negative y direction.

Substitute for N and for. Therefore, the maximum allowed weight of the unit is. Calculate the work done by the force on the object. Use the definition of the work W done on an object by a force over a displacement.

The displacement and weight force along the roof both act in the same direction, the negative x direction, so reduce W to simple multiplication of the magnitudes F and s:. The magnitude of the weight acting along the roof in the direction is,. Substitute for F in the equation and solve for. Substitute for w , for s , and for in W:. Therefore, the work done on the unit by the weight force during its slide is. Solutions Manuals are available for thousands of the most popular college and high school textbooks in subjects such as Math, Science Physics , Chemistry , Biology , Engineering Mechanical , Electrical , Civil , Business and more.

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