Chapter 9:  Equilibrium Elasticity, and Fracture

 

The title of the chapter contains the three main topics of the chapter.

 

Required:

Question:  1, 2, 6, 18

Problems:  27, 47, 81, Check I, and Reality Check II (Problems are on the next page)

Reality Check

 

Suggested:

 

Questions:  If you move a post around on a cantilever, how do the forces provided by each post change.

Problems:  7, 17, 50, 56, 82, and any other problems that deals with equilibrium, elasticity, and strength.

 

Answers: 

50.  9.5 x 106 N/m2. 

56.  392.7 N

82. Cannot walk to the left side (the right hand rope would need to push down)

      Can walk to the right side (the left rope still pulls up)

 

 

Reality Check #1 – I was talking to my wife’s boss, who is an orthopedic surgeon.  He said at one time if a person injured their hip, they were not allowed to put any of their weight on that leg when they were standing.  If you did this, the center of mass for your leg would be right below your hip socket as shown in figure a.  He said that now people can gently rest their leg on the floor.  By doing so, it reduces the force on the hip (FR), allowing for a faster healing.  If you gently rest your leg on the floor as shown in figure b, the floor pushes up with a force equal to the weight of the leg, WL.  Here is the problem, from the diagrams and the forces given show that in diagram b there is less force on the hip (FR).  You can assume the leg has a mass of 1.   Assume the angle between Fm and the vertical is 19 degrees for both pictures.  Note:  Some of the forces in the diagram turn out to be zero; you cannot assume any of them are zero before you start.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


Reality Check #2 – In class I told you that orthopedic surgeon hold a broken femur (thigh bone) together with a metal plate that is screwed to the femur above the break and below the break.  If you are a biomechanical engineer and you want each screw to hold 500% of the person’s weight and you wanted to make it out of steel. How big should you make it.  Write your answer in terms of the diameter of the screw.  Check to see if your answer is reasonable, by comparing its size to the size of the femur.  Hint: what “type” of forces are present on the screw.  Use approximations where necessary.