Basic Physics (Newton's First Law of Motion / Dynamics)

Question

Please do provide me a clear and detailed step-by-step solution and a final answer.

A block is suspended from a rope tied to two other ropes. One rope is horizontally attached to a wall and the other is fastened to the ceiling. The angle between ceiling and the rope is 45°. What are the tensions in each of the ropes? Assume the weights of the ropes and the knot are negligible. If the weight of the block is 120 N, what is the tension in the ceiling rope?

This is my first time encountering a Dynamic and/or Newton's First Law Problem, Thank you so much!

Answer 1

First we draw a free body diagram (by text here) of the the block of weight 120 N.

There are 3 forces acting on the block.

The 1st force is the tension of the rope horizontally attached to a wall. Let it be W. Force direction: As it doesn't mention in the question, assume that it is to the right.

The 2nd force is the tension of the rope fastened to the ceiling with the angle between ceiling and 45°. Let it be C. Force direction: When W is to the right, C should be to the upper left direction

The 3rd force is the weight of the block. Force direction: downwards due to gravity

As C is a force pointing upper left direction, it can be resolved into x(Horizontal) and y (vertical) components by trigonometry.

Cx(horizontal component of C, force pointing to the left) = C cos 45°

Cy(vertical component of C, force pointing upwards) = C sin 45°

As it mentioned "suspended" in the question, the system is in Static Equilibrium. So the net force should be zero / all forces are balanced according to the Newton's first law of motion

Cy(the vertical component of C) = weight of the block (As it is suspended, these two forces are in opposite direction but same magnitude.)

C sin 45° = 120

C = 187 N