Question

A 40.0-kg uniform platform is suspended by two cables, 2.00m apart, where the center of the platform lies midway between the cables. A 5.00-kg paint bucket is placed on the platform, 24.0cm to the right of the right cable, as shown in Figure A2.15. What is the tension in each cable?

A 40.0-kg uniform platform is suspended by two cables, 2.00 m apart, where the centre of the platform lies midway between the cables. A 5.00-kg paint bucket is placed on the platform, 24.0 cm to the right of the right cable, as shown in Figure A2.15. What is the tension in each cable? 2.0m 24 cm

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Forces acting on the platform are, ) Weight of the platform, Mg vertically downwards acting at 1.00 m from the left cable. ii) Tension in the first string 1, vertically upwards, acting at point of left cable. ii) Tension in the second string 12, vertically upwards, acting at 2.00 m from the left cable. ii) Weight of the bucket mg, vertically downwards, acting at 2.24 m from the left cable. Net force on the platform is zero, T + 12 = 40.0 * 9.81 5.00 * 9.81 = 441 N Torque about the point where left cable is attached to the plank is, (torque due to 1 is zero) Mg 1.00+mg 2.24 - T2 2.00 40.0 * 9.81 * 1.00 + 5.00 * 9.81 * 2.24 = T2 * 2.00 (since M 40.0 kg m = 5.00 kg T2-251 N T1 = 441-T2 = 441-251 = 190 N Tensions in the two cables are Ti T251 N 190 N and

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