(Real-life Example from Bill's Life) Assume that one evening you are out riding your bike and...

   

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(Real-life Example from Bill's Life) Assume that one evening you are out riding your bike and you come to a big hill. You decide that you want to race your brother down the hill going as fast as you each possibly can-but at the bottom of the hill is an unexpected speedbump that you hit going 55mph. This causes your bike's center of mass to rotate up and over the speedbump and you land at full force on your left humorous - shattering it into multiple shards. At the hospital, the orthopedic surgeon has to reconstruct the elbow using bone putty and multiple plates and screws. After the surgery is over and prior to starting Physical Therapy the surgeon says: "Since your bicep detached during the accident, until the elbow fully heals it has a maximum force tolerance of 15 Newtons (which could rip the tendon from the hook embedded in the radial head) ... so the maximum weight that can be carried with the left arm for now is 18.4 grams"; but you are a physicist- and you want to figure out if that is really the case or not, so you build the following lab apparatus to check if the surgeon really did his math correctly... Force probe F pivot point bicep Tbicep Obicep farm marmg ILoad mass mLoadg Assume that for the experiment, you always kept the "arm" to be level. That is, you setup the arm to be perfectly perpendicular to the acceleration due to gravity. This was done intentionally to greatly simplify the calculation for the torques due to the load and the arm. Recall that the definition of torque is given by: 7=FxF and |=|||| sin(0) After making several measurements, and calibrating the force sensor correctly, you come up with the following values for the left arm: Marm = 52.3g mload = 18.4 g Garm = 270º (+8) Farml = 227.5 mm load] = 430 mm load = 270º (+8) |bicep | = 85 mm #bicep = variable 13a. In the apparatus above, how many torques are in the system and what creates each torque? 13b. Assuming that the system is in static equilibrium, write an equation for Newton's 3rd Law for a static rotating system. 13c. Using the definition of Torque given above, write down and simplify an equation for ceed to of the torque vectors identified in 13a. Remember, to find the direction of the torque, we need to use the right-hand rule. Also, which direction of rotation (clock-wise or counter-clock-wise) do each of the torques create? 13d. Use the equations from 13c and Newton's 3rd Law from 13b to find an expression for the Force on the bicep as a function of the other variables given above part 13a. 13e. Fill out the following table for the various angles of the bicep: Theta-Bicep Deg] 45° 60⁰ 90° 120° Force on the Bicep IN 13f. Was the surgeon correct and why do you think he say what he did? (Real-life Example from Bill's Life) Assume that one evening you are out riding your bike and you come to a big hill. You decide that you want to race your brother down the hill going as fast as you each possibly can-but at the bottom of the hill is an unexpected speedbump that you hit going 55mph. This causes your bike's center of mass to rotate up and over the speedbump and you land at full force on your left humorous - shattering it into multiple shards. At the hospital, the orthopedic surgeon has to reconstruct the elbow using bone putty and multiple plates and screws. After the surgery is over and prior to starting Physical Therapy the surgeon says: "Since your bicep detached during the accident, until the elbow fully heals it has a maximum force tolerance of 15 Newtons (which could rip the tendon from the hook embedded in the radial head) ... so the maximum weight that can be carried with the left arm for now is 18.4 grams"; but you are a physicist- and you want to figure out if that is really the case or not, so you build the following lab apparatus to check if the surgeon really did his math correctly... Force probe F pivot point bicep Tbicep Obicep farm marmg ILoad mass mLoadg Assume that for the experiment, you always kept the "arm" to be level. That is, you setup the arm to be perfectly perpendicular to the acceleration due to gravity. This was done intentionally to greatly simplify the calculation for the torques due to the load and the arm. Recall that the definition of torque is given by: 7=FxF and |=|||| sin(0) After making several measurements, and calibrating the force sensor correctly, you come up with the following values for the left arm: Marm = 52.3g mload = 18.4 g Garm = 270º (+8) Farml = 227.5 mm load] = 430 mm load = 270º (+8) |bicep | = 85 mm #bicep = variable 13a. In the apparatus above, how many torques are in the system and what creates each torque? 13b. Assuming that the system is in static equilibrium, write an equation for Newton's 3rd Law for a static rotating system. 13c. Using the definition of Torque given above, write down and simplify an equation for ceed to of the torque vectors identified in 13a. Remember, to find the direction of the torque, we need to use the right-hand rule. Also, which direction of rotation (clock-wise or counter-clock-wise) do each of the torques create? 13d. Use the equations from 13c and Newton's 3rd Law from 13b to find an expression for the Force on the bicep as a function of the other variables given above part 13a. 13e. Fill out the following table for the various angles of the bicep: Theta-Bicep Deg] 45° 60⁰ 90° 120° Force on the Bicep IN 13f. Was the surgeon correct and why do you think he say what he did?

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To write down the equations for each of the torque vectors identified in 13a well use the definition of torque as the cross product of the position ve... View the full answer