The lubrication of bone joints is a subject of ongoing medical research. Two bones connected at a joint do not touch. The bones are covered in articular cartilage, and are surrounded by lubricating synovial fluid. Rheumatoid arthritis results in overproduction of synovial fluid, swollen joints, and difficult and painful movement. Other joint disorders degrade the synovial fluid, directly increasing the friction between the bones, resulting in painful motion.

Figure$1$ of $1$

The graph shows force F h as a function of force F d$.$ Force F d is measured from $0$ to $1000$ newtons on the x$-$axis and force F h is measured from $0$ to $16$ newtons on the y$-$axis. Five dots with the following approximate coordinates are marked on the graph: $180$ newtons and $1\mathrm{.}8$ newtons, $320$ newtons and $3\mathrm{.}8$ newtons, $500$ newtons and $5$ newtons, $800$ newtons and $7$ newtons, $1000$ newtons and $9$ newtons.

Part A

To measure the effective coefficient of friction in a bone joint, a healthy joint $($and its immediate surroundings$)$ can be removed from a fresh cadaver. The joint is inverted, and a weight is used to apply a downward force F$$ d

on the head of the femur into the hip socket. Then, a horizontal force F$$ h

is applied and increased in magnitude until the femur head rotates clockwise in the socket. The joint is mounted in such a way that F$$ h

will cause clockwise rotation, not straight$-$line motion to the right. The friction force will point in a direction to oppose this rotation.

Draw vectors indicating the normal force n$$

$($magnitude and direction$)$ and the frictional force f$$ f

$($direction only$)$ acting on the femur head at point A$.$ Assume that the weight of the femur is negligible compared to the applied downward force.

Draw the vectors starting at the black dot. The location, orientation and relative length of the vectors will be graded.

View Available Hint$($s$)$for Part A

Select the elements from the list and add them to the canvas setting the appropriate attributes.Select to observe the list of the elements that can be added to the canvas. Press CTRL$+$Y to get to the elements on the canvas. Press CTRL$+$Q to quit the application.

Select to show$/$hide the vector for the sum of the drawn vectors. Press CTRL$+$Y to get to the elements on the canvas. Press CTRL$+$Q to quit the application.

Delete the selected element. Press CTRL$+$Y to get to the elements on the canvas. Press CTRL$+$Q to quit the application.

Press to go to keyboard navigation instructions below the canvas.

Select to remove all drawn elements. Press CTRL$+$Y to get to the elements on the canvas. Press CTRL$+$Q to quit the application.

Attributes panel is empty. Press CTRL$+$Y to get to the elements on the canvas. Press CTRL$+$M to return to the main menu. Press CTRL$+$Q to quit the application.No elements selected

The length is $8$ units. The angle counting from horizontal axis counterclockwise $0$ degrees. Use arrows to move the vector.

Press TAB to go to the next element. There is an image on the canvas: A bone joint consists of a femur head above and a hip socket below. A black dot is at point A$,$ positioned at the lowest point of the femur head. A horizontal rightward force F h and a vertical downward force F d act on the femur head.

A bone joint consists of a femur head above and a hip socket below. A black dot is at point A$,$ positioned at the lowest point of the femur head. A horizontal rightward force F h and a vertical downward force F d act on the femur head.

F$$ d

F$$ h

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 c