Question

A 850N painter stands 1.2m from on end of a 3.0m scaffold supported at each end by a step ladder. The scaffold weighs 250N and there is a 40.0N paint can .50m from the end opposite the painter. How much force is exerted by each step ladder?

Answer 1

Question

We will have next equations:

For the left end of the ladder:

$$\begin{array}{l} R_{\text{right}} \cdot 3 = 850 \cdot 1.2 + 250 \cdot 1.5 + 40 \cdot 2.5 = 1020 + 375 + 100 = 1495(N \cdot m) \Rightarrow \\ \Rightarrow R_{\text{right}} = \frac{1495(N \cdot m)}{3(m)} = 498.3(N). \end{array}$$

And for the sum of the forces at equilibrium:

$$R_{\text{right}} + R_{\text{left}} = 850 + 250 + 40 = 1140(N) \Rightarrow R_{\text{left}} = 1140(N) - 498.3(N) = 641.7(N).$$

Answer: 641.7(N).