# Application of Newton's Laws to Systems of Masses with Ropes

Solve for No. 1 to No. 5 Tension (forces)

Tension = ?

(See attached file for diagrams)

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#### Solution Preview

To solve these problems, we apply Newton's second law at each junction of ropes. Since each of these problems is static, the sum of forces, due to the tensions in each rope, must be zero in each case. We solve these problems by looking at the x-compent (horizontal) and y-component (vertical) of the forces at each junction.

28. Clearly we have T1 = 100 pounds, since the tension in rope 1 is holding up the 100-pound weight.

To solve for T2 and T3, first note that they are equal by symmetry. Considering the z-component of the forces acting on junction 123, we find

-T1 + (T2 + T3) sin 45 = 0

-100 + 2 T2 sqrt(2)/2 = 0

T2 sqrt(2) = 100

T2 = T3 = 100/sqrt(2) = 70.7 ...

#### Solution Summary

This solution helps with the application of Newton's Laws to systems of masses with ropes. We show how to calculate tension in ropes for given systems of masses and ropes, using Newton's laws. Step by step calculations with explanations are given.