Newton's laws - Block hanging from two ropes

Problem Statement:

We assume that each rope of the figure can support a maximum tension T = 50N and that α = 60º. Determine the maximum mass of the block of the figure so that the ropes do not break.

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Solution:

To solve this problem we apply Newton’s second law. First we represent the forces acting on the block (the weight and tension of each rope) and we choose the axes to make the projections:

Newton’s second law for this situation is:

The second member of the equation is zero because when the block is at rest it has no acceleration.

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Projecting on the axes we get:

From equation (1) we can deduce that the tensions of the ropes are equals:

And after substituting in equation (2) we obtain the value of the mass:

In the problem we have used g = 10 m/s2

Do not forget to include the units in the results of the problems.

When projecting Newton’s second law on the axes, you must take into account the sign of each projection. That is why it is important to define what are the Cartesian axes of the reference frame and what is the positive direction for each one.

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