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57 -kg packing crate is pulled with constant speed across a rough floor with a rope that is at an angle of $37^{\circ}$ above the horizontal. If the tension in the rope is 142 $\mathrm{N}$ , how much work is done on the crate to move it 6.1 $\mathrm{m}$ ?

Work $=691.77 \mathrm{J}$

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Cornell University

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

Numerade Educator

Okay, So a 57 kilogram packing crate is pulled with constant speed across a rough floor. Okay, so this is the packing crate. It's on our floor, Um, by a rope, that is an angle of 37 degrees above the horizontal. Okay, so that means this angle right here is 37 degrees. Okay, if the tension in the rope is 142 Nunes. Okay, So this is the rope, and the tension in the rope is going to be 100 and 42 nudes. All right, how much work is done on the crate to move its 6.1 meters? Okay, so we have to find the work. So the work is gonna be the force times the distance. But we have to be careful and get the component of force that acts parallel to the displacement. Okay, So that component of the force all right, um, our net force, like the total strength of this force on the rope, is 142 but then we just want this x component of it. Okay, over here. And how do we get that? Well, that is just gonna be 1 42 times the co sign of 37 times the coastline of 37 degrees. All right, and we're moving the create 6.1 meters. Okay, so we do this calculation 142 times Coast under 37 degrees times 6.1, and that gives us 691.77. Jules, okay.