a 200 N wooden platform is suspended from the roof of the house by ropes attached to it's ends. it has a total length of 4.2 meters. a painter weighing 650 N stands from the left end of the platform. find the tension in each end of the ropes .

Sum of Forces and Torques is zero.

T1 + T2 = 650 + 200
200(2.1) + 650(number omitted) - T2(4.2) = 0
Use 2nd to find T2, plug into first for T1.

To find the tension in each end of the ropes, we need to analyze the forces acting on the platform.

Let's assume that the left end of the platform is point A and the right end is point B.

First, let's consider the forces acting on the painter at point A:
1. Weight of the painter (650 N) acting vertically downward.
2. Tension force in the rope at point A acting vertically upward.

Since the painter is standing at rest on the platform, these two forces must balance each other out. So we can say:

Tension at A = Weight of the painter = 650 N

Now, let's consider the forces acting on the platform itself:
1. Weight of the platform (200 N) acting vertically downward.
2. Tension force in the rope at point A acting horizontally to the right.
3. Tension force in the rope at point B acting horizontally to the left.

Since the platform is at rest, the vertical forces must balance out, and the horizontal forces must also balance out. Therefore, we can say:

Vertical forces:
Tension at A = Weight of the platform

Horizontal forces:
Tension at A = Tension at B

Now, let's find the weight of the platform:

Weight of the platform = Mass x Acceleration due to gravity
= (200 N) / (9.8 m/s^2) [assuming g ≈ 9.8 m/s^2]
= 20.41 kg

Now we can substitute the known values into our equations:

Tension at A = 20.41 kg x 9.8 m/s^2
= 200 N

Therefore, the tension in the rope at point A is 200 N.

Since the horizontal forces must balance out:
Tension at A = Tension at B
200 N = Tension at B

Therefore, the tension in the other end of the rope (point B) is also 200 N.

So, the tension in each end of the ropes is 200 N.