A bar with length `, and mass m is held horizontally by two massless cords as in Figure 1. The bar has non-uniform density, so its center of mass xcm is not necessarily at the center of the bar. The left cord attaches to the wall with angle θ, the right with angle φ. Express all answers in terms of m, g, φ, and θ (or subsets thereof). (i) Draw a diagram with all forces on the bar at their respective locations. (ii) What is the tension in the left cord? Give your answer in terms of m, g, θ, and φ. (iii) What is the tension in the right cord? Give your answer in terms of m, g, θ, and φ. (iv) What is the location of the bar’s center of mass xcm relative to the left most point of the bar (as indicated in Figure 1).
3) A bar with length `, and mass m is held horizontally by two massless cords as in Figure 1. The bar has non-uniform density, so its center of mass xcm is not necessarily at the center of the bar. The left cord attaches to the wall with angle θ, the right with angle φ. Express all answers in terms of m, g, φ, and θ (or subsets thereof).
(i) Draw a diagram with all forces on the bar at their respective locations.
(ii) What is the tension in the left cord? Give your answer in terms of m, g, θ, and φ.
(iii) What is the tension in the right cord? Give your answer in terms of m, g, θ, and φ.
(iv) What is the location of the bar’s center of mass xcm relative to the left most point of the bar (as indicated in Figure 1).
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