Midterm Exam 1 Biomechanics IPHY 4540 Spring 2009 circle your TA/lab section Molly Kelly Print Name_______________________________________ You must draw large enough for us to grade and write clearly enough for us to read! BOLD print means you must do something On my honor, as a University of Colorado at Boulder student, I have neither given nor received unauthorized assistance on this work. ______________________________ sign name Question 1 1A. Imagine a skier on a ski lift with her legs dangling. Diagram and explain how the ankle is a musculoskeletal lever system. Indicate the location of the muscle (M), joint (J), load (L), and what is being amplified. Name the primary muscle. 1B. The loading in figure 1, is commonly experienced during a forward fall while skiing and could potentially result in fracture of the tibia. Indicate on the diagram the type of bending stresses and their location on the tibia (T and C). Also indicate where the tibia is most likely to break and on which side. Explain why. Assume the skier is a young adult. Isometric contraction of which muscle would reduce the bending stresses on the tibia? 1C. Children often experience green‐stick fractures, where the bone bends before it breaks. What is the technical term used to describe this property? What differences in the material composition of bone, compared to a young adult, are most likely responsible? Use stress­strain curves to explain. Would you be more confident of the location of the fracture in part 1B if the skier was a child? 1D. In the diagram below is a representation of cortical bone remodeling with age in men in the femoral middiaphysis. Between ages 25 and 85, ro changes from 1.5 cm to 1.75 cm, and ri from 0.75cm to 1.0cm. Calculate the change in cross­sectional area. Use equations to show: i) why this change is beneficial ii) what other age­related changes may cancel out these benefits Question 2 2A. Imagine you have 10 sarcomeres; each generates a maximum of 1 unit of force, and shortens with a maximum velocity of 1 unit/s. Diagram an arrangement of sarcomeres that will create a muscle fiber with the following force and velocity characteristics. Use I to represent individual sarcomeres, and draw ellipses around sarcomeres to specify fibers. i) Fmax= 5 units; Vmax= 2 units/s ii) Fmax= 2 units; Vmax=5 units/s iii) Fmax=5cos10o units; Vmax=2cos10o units/s iv) Fmax=5sin10 o units; Vmax=2sin10 o units/s 2B. Which of the muscles above (i,ii,iii,iv) would you be least likely to see in the human body? Explain why. 2C. On a single graph, draw the force­velocity curves for the four muscles above in absolute units. Be sure to label the axes appropriately (with units). Only draw the shortening velocity half of the graph (positive velocity) 2D. On a single graph, draw the force­velocity curves for the four muscles above in normalized units. Be sure to label the axes appropriately (with units). Only draw the shortening velocity half of the graph (positive velocity) Question 3 3A. Give three examples (including graphs) of viscoelastic properties of tendon. Be sure to explain the examples in terms of the conditions under which the data were obtained. 3B. Oscar Pistorius, a double below‐knee amputee, was initially not allowed to run in the able‐bodied 2008 Olympics because it was determined that his prosthetic running limbs gave him an advantage over able bodied runners. Below is a loading‐unloading curve for the Achilles tendon in a healthy athlete, and a hypothetical loading‐unloading curve for Pistorius’ prosthetic limb. Using technical terms, describe one property that has the same value in both curves, and one property that has different values. Based on these two curves alone, explain why Pistorius may or may not have an advantage. Question 4 4A. A quarterback releases a football with a linear velocity of 30 m/s. How far will it go, if he releases it at a height of 2.0m and with a 10o release angle (with respect to horizontal)? 4B. Name three factors the quarterback can change to increase the horizontal distance covered by the pass. Pick one, increment it by 10%, and use calculations to prove its effect on horizontal distance. 4C. If a wide‐receiver wanted to catch the ball in the endzone 40 yards (37 meters) away from the quarterback, how high do his hands need to be in order to catch the ball? (Use the conditions specified in part 4A) 4D. The wide‐receiver is 10 yards (9 m) away from the endzone when the quarterback throws the ball. If he starts running the instant the quarterback releases the ball, what does his average running speed need to be in order to catch the ball in the endzone at the height calculated in part C? 4E. Based on your knowledge of locomotion kinematics, why may the wide­receiver still miss the pass?