A pair of students are lifting a heavy trunk on move$-$in day. $($Figure $1)$ Using two ropes tied to a small ring at the center of the top of the trunk, they pull the trunk straight up at a constant velocity v$$

$.$ Each rope makes an angle $\backslash$theta

with respect to the vertical. The gravitational force acting on the trunk has magnitude FG

$.$

Figure$1$ of $1$

The figure shows a pair of students symmetrically lifting a trunk using two ropes. The ropes are tied to a small ring at the center of the top of the trunk.

The trunk is moving at a constant velocity. This means that you can model it as a particle in dynamic equilibrium. Furthermore, you can ignore the masses of the ropes and the ring because it is reasonable to assume that their combined weight is much less than the weight of the trunk.

Part A

Part complete

The most convenient coordinate system for this problem is one in which the y axis is vertical and the ropes both lie in the xy plane, as shown below. Identify the forces acting on the trunk, and then draw a free$-$body diagram of the trunk in the diagram below. The black dot represents the trunk as it is lifted by the students.

Draw the vectors starting at the black dot. The location and orientation of the vectors will be graded. The length of the vectors will not be graded.

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The angle counting from horizontal axis counterclockwise $271\mathrm{.}2$ degrees. Use arrows to move the end point.

Press TAB to go to the next element. There is an image on the canvas: Two ropes are tied to the center of the top of a trunk. The x y axes have the origin at the tying point. The x axis is directed horizontally rightward. The y axis is directed vertically upward. Each rope goes upward from the origin and makes an angle of $48$ degrees with the y axis. A black dot is at the origin.

Two ropes are tied to the center of the top of a trunk. The x y axes have the origin at the tying point. The x axis is directed horizontally rightward. The y axis is directed vertically upward. Each rope goes upward from the origin and makes an angle of $48$ degrees with the y axis. A black dot is at the origin.

T$1$

T$2$

F$$ G

Select the elements from the list and add them to the canvas setting the appropriate attributes. Press TAB to get to the main menu.Use arrow keys to apply parallel transition to the object. Press TAB to move to the next element on the canvas. Press SHIFT$+$TAB to return to selecting the end point. Press DEL to delete the element from the canvas. Press CTRL$+$A to modify the attributes. Press CTRL$+$M to get to the main menu. Press ESC to quit adding or editing this element. Press CTRL$+$Q to quit the application.Press SPACE to get to the set of hotspots or use arrow keys to move on the canvas. Press ESC to quit adding or editing this element. Press CTRL$+$A to modify the attributes. Press CTRL$+$M to get to the main menu. Press CTRL$+$Q to quit the application.Press SPACE to get to the set of hotspots or use arrow keys to move on the canvas. Press TAB to select the whole element. Press SHIFT$+$TAB to move to selecting the start point. Press CTRL$+$A to modify the attributes. Press CTRL$+$M to get to the main menu. Press ESC to quit adding or editing this element. Press CTRL$+$Q to quit the application.Press TAB to move to the next element on the canvas. Press DEL to delete the element from the canvas. Press CTRL$+$A to modify the attributes. Press CTRL$+$M to get to the main menu. Press ESC to quit adding or editing this element. Press CTRL$+$Q to quit the application.Press SPACE to get to the set of hotspots or use arrow keys to move on the canvas. Press ENTER to change the direction. Press TAB to move to the next element on the canvas. Press DEL to delete the element from the canvas. Press CTRL$+$A to modify the attributes. Press CTRL$+$M to get to the main menu. Press ESC to quit adding or editing this element. Press CTRL$+$Q to quit the application.

Previous Answers

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Part B

In the free$-$body diagram drawn in the previous part, different symbols are used to represent the tensions in the two ropes. This notation could be simplified by identifying a useful relationship between these two forces. W