Question

4) Read the following and revise your free body diagram as necessary A common confusion when drawing extended free body diagrams is how to draw the force of gravity. For a static equilibrium situation like this, you should draw a single arrow to represent the force of gravity on an extended object. The tail of this vector is placed at the center of mass of the object. It is good practice to pause at this point and think about whether the directions of the forces you drew are consistent with static equilibrium. Thinking of the shoulder joint as the axis of rotation, in what sense (CW, CCW, or zero) are the torques due to each of the forces you drew? Is it possible for all the torques to balance out? What if you thought of the center of mass of the arm as the axis of rotation? Will the forces you drew enable Fnet, and Fnet, y to be zero? Suppose your "knowns" include: The mass of the arm (m) The distance from the shoulder joint to the arm's center of mass (D) The distance from the shoulder joint to the deltoid's attachment point (d) The angle between the deltoid and the arm (0) Your "unknowns" include: The magnitude of the force on the arm by the deltoid (F) The x and y components of the force on the arm by the shoulder joint (N, and N,) 5) Choosing the shoulder joint as the axis of rotation, fill in the static equilibrium condition for torques: 0 with the details of this problem and then solve for F. Your answer should be an expression in terms of the "knowns". 6) Plug in the values m = 4.0 kg, D 38 cm, d 17 cm, and 0 15" to find a value for F. 7) The force of the deltoid is greater than / less than (circle one) the weight of the arm. Use the idea of "lever arm" to explain why this answer makes sense. 8) Now consider the force on the arm by the shoulder joint. For Fnet, x and Fnet, y to both be zero, the shoulder joint must pull to the left / push to the right (circle one) on the arm, and the shoulder joint must push down / up (circle one) on the arm. 9) Does your extended free body diagram need a revision? If so, do that now. 10) Fill in the static equilibrium conditions for forces, Faet, x 0 and Fnet, y 0, with the details of this problem and then solve for N, and Ny. Your answers should be expressions in terms of the "knowns" 11) Plug in the values given on the previous page for the "knowns" to find values for N, and Ny. 12) As a final test to see if you've made any mistakes, treat the center of mass of the arm as the axis of rotation and compute Tnet E t. If you haven't made any mistakes, this sum should be zero (because it's a static equilibrium situation!)

Answer 1

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