A 75kg painter stands on a 5.5m long uniform plank resting on a scaffold. If the plank's mass is 20kg , how close to the left end of the plank can he stand without tipping the plank? ( The scaffold supports are 2.5m apart, and the plank extends beyond the scafold supports, 1.5m on each end.)
The mass of the plank on the left side of the scaffold is: M? = (20 kg) × (1.5 m) / (5.5 m) = 5.45 kg The distance between the scaffold and the center of mass on the left side is: L? = (1.5 m) / 2 = 0.75 m So the torque of the plank on the left side is: T? = (5.45 kg)×(0.75 m) = 4 kgm The mass of the plank on the right side of the scaffold is: M? = (20 kg) × ((5.5 m) - (1.5 m)) / (5.5 m) = 14.5 kg The distance between the scaffold and the center of mass on the left side is: L? = ((5.5 m) - (1.5 m)) / 2 = 2 m So the torque of the plank on the left side is: T? = (14.5 kg)×(2 m) = 29 kgm Now, say the painter stands at X meter on the left side from the scaffold, so the torque added on the left side is: T? = X × (75 kg) The total torque on the left must be the same as the total torque on the right, so (4 kgm) + X×(75 kg) = (29 kgm) X×(75 kg) = (25 kgm) X = 0.333 m That is the maximum distance the painter can move away from the scaffold, so the distance to the end of the scaffold is: D = (1.5 m) - (0.333 m) = 1.167 m < - - - - - - answer
