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A uniform plank of wood is balanced 30cm from one end when a lead of 0.08kg is hung at 0mark end . calculate the weight of the plank
A uniform plank of wood is balanced 30cm from one end when a lead of 0.08kg is hung at 0mark end . calculate the weight of the plank
Answers
GPT 3.5
To balance the plank with the lead at 0 mark, the plank must exert a torque equal to the torque exerted by the lead.
The torque exerted by the lead is given by the formula:
Torque = Force x Distance
Torque = 0.08kg x 9.8m/s^2 x 0.30m
Torque = 0.2352 Nm
Since the plank is balanced at 30cm from one end, and the lead is at the 0 mark end, the center of mass of the plank must be at the midpoint of the plank.
Let x be the distance from the center of mass of the plank to the point where the lead is hung. Since the plank is uniform, the weight of the plank can be modelled as acting at the center of mass of the plank.
The torque exerted by the plank is given by the formula:
Torque = Weight of plank x Distance
Weight of plank x 0.30m = 0.08kg x 9.8m/s^2 x x
0.3 x Weight of plank = 0.0784 x
Weight of plank = 0.0784/0.3
Weight of plank = 0.2613 kg
Therefore, the weight of the plank is 0.2613 kg or 261.3 grams.
The torque exerted by the lead is given by the formula:
Torque = Force x Distance
Torque = 0.08kg x 9.8m/s^2 x 0.30m
Torque = 0.2352 Nm
Since the plank is balanced at 30cm from one end, and the lead is at the 0 mark end, the center of mass of the plank must be at the midpoint of the plank.
Let x be the distance from the center of mass of the plank to the point where the lead is hung. Since the plank is uniform, the weight of the plank can be modelled as acting at the center of mass of the plank.
The torque exerted by the plank is given by the formula:
Torque = Weight of plank x Distance
Weight of plank x 0.30m = 0.08kg x 9.8m/s^2 x x
0.3 x Weight of plank = 0.0784 x
Weight of plank = 0.0784/0.3
Weight of plank = 0.2613 kg
Therefore, the weight of the plank is 0.2613 kg or 261.3 grams.