two painters stand on a 10.00m scaffold. one,of mass 65.0kg, stands 2.00m from one end. the other, of mass 95.0kg, stands 4.00m from the other end. they share a paint container of mass 18.0kg located between the two and 2.50m from the larger person. what weight must be supported by each of the ropes secured at yhr ends of the scaffold?

Question

two painters stand on a 10.00m scaffold. one,of mass 65.0kg, stands 2.00m from one end. the other, of mass 95.0kg, stands 4.00m from the other end. they share a paint container of mass 18.0kg located between the two and 2.50m from the larger person. what weight must be supported by each of the ropes secured at yhr ends of the scaffold?

Answer 1

To determine the weight that each rope must support, we need to calculate the net torque acting on the scaffold about the point where the left rope is attached and the point where the right rope is attached.

First, let's calculate the torques due to the painters.

The torque (τ) exerted by a force (F) at a perpendicular distance (r) from the axis of rotation is given by the equation τ = F * r.

For the painter with a mass of 65.0 kg, standing 2.00 m from one end of the scaffold:
The torque exerted by the painter's weight is τ1 = (m1 * g) * r1, where m1 is the mass of the painter, g is the acceleration due to gravity (approximately 9.8 m/s²), and r1 is the distance of the painter from the left end.
Substituting the given values, τ1 = (65.0 kg * 9.8 m/s²) * 2.00 m.

Similarly, for the painter with a mass of 95.0 kg, standing 4.00 m from the other end of the scaffold:
The torque exerted by the painter's weight is τ2 = (m2 * g) * r2, where m2 is the mass of the painter, g is the acceleration due to gravity, and r2 is the distance of the painter from the right end.
Substituting the given values, τ2 = (95.0 kg * 9.8 m/s²) * 4.00 m.

Next, let's calculate the torque due to the paint container.

The torque exerted by the paint container is τ3 = (m3 * g) * r3, where m3 is the mass of the paint container, g is the acceleration due to gravity, and r3 is the distance of the container from the left end.
Substituting the given values, τ3 = (18.0 kg * 9.8 m/s²) * 2.50 m.

Now, let's add up all the torques and set them equal to zero because the scaffold is in equilibrium (i.e., not rotating). The sum of the torques is equal to zero:

τ1 + τ2 + τ3 = 0

(65.0 kg * 9.8 m/s² * 2.00 m) + (95.0 kg * 9.8 m/s² * 4.00 m) + (18.0 kg * 9.8 m/s² * 2.50 m) = 0

Simplifying this equation will give us the weight that each rope must support.