You need to measure the mass M of a 4.00-m long bar. The bar has a square cross section but has some holes drilled along its length, so you suspect that its center of gravity isn€™t in the middle of the bar. The bar is too long for you to weigh on your scale. So, first you balance the bar on a knife-edge pivot and determine that the bar€™s center of gravity is 1.88 m from its left-hand end. You then place the bar on the pivot so that the point of support is 1.50 m from the left-hand end of the bar. Next you suspend a 2.00-kg mass (m₁) from the bar at a point 0.200 m from the left-hand end. Finally, you suspend a mass m₂= 1.00 kg from the bar at a distance x from the left-hand end and adjust x so that the bar is balanced. You repeat this step for other values of m₂and record each corresponding value of x. The table gives your results.

(a) Draw a free-body diagram for the bar when m₁ and m₂ are suspended from it.

(b) Apply the static equilibrium equation Σt_z = 0 with the axis at the location of the knife-edge pivot. Solve the equation for x as a function of m₂.

(c) Plot x versus 1/m₂. Use the slope of the best-fit straight line and the equation you derived in part (b) to calculate that bar€™s mass M. Use g = 9.80 m/s².

(d) What is the y-intercept of the straight line that fits the data? Explain why it has this value.

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2.50 1.50 4.00 2.00 3.00 m2 (kg) | 1.00 (m) 2.83 2.00 3.50 2.50 2.32 2.16 x