Answer:
The force on the left cable is 1000 N, and the force on the right cable is 1490 N.
Explanation:
Since the scaffold is in rotational and translational equilibrium, the net force and the net torque on the scaffold are both zero. Begin by drawing a free body diagram of the scaffold, which shows all the forces and their locations. There are six forces:
- Tension force T₁ pulling up at the left cable
- Bob's weight 795 N pulling down 1.00 m from the left
- Scaffold's weight 315 N pulling down at the center, 1.50 m from the left
- Equipment weight 500 N pulling down 2.00 m from the left
- Joe's weight 880 N pulling down 0.500 m from the right, or 2.50 m from the left
- Tension force T₂ pulling up at the right cable, 3.00 m from the left
The scaffold is in translational equilibrium, so the net force is zero.
∑F = 0
T₁ − 795 − 315 − 500 − 880 + T₂ = 0
T₁ + T₂ = 2490
The scaffold is in rotational equilibrium, so the net torque about the left end is zero. Remember that torque is force times perpendicular distance.
∑τ = 0
T₁ (0) − 795 (1.00) − 315 (1.50) − 500 (2.00) − 880 (2.50) + T₂ (3.00) = 0
T₂ (3.00) = 4467.5
T₂ = 1490 N
Substitute into the first equation.
T₁ + 1490 = 2490
T₁ = 1000 N
Therefore, the force on the left cable is 1000 N, and the force on the right cable is 1490 N.
