Consider the 668 N weight held by two cables shown below. The left-hand cable had tension T2 and makes an angle of pheta 2 with the ceiling. The right-handed cable had tension 550 N and makes an angle 45 degrees with the ceiling. The right hand cable makes an angle of 45 degrees with the ceiling and has a tension of 550 N.

A.) what is the Tension T2 in the left- hand cable slanted at an angle of pheta 2 with respect to the wall? Answer in units of N

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To find the tension T2 in the left-hand cable slanted at an angle of θ2, we can use the concept of resolving forces.

First, let's break down the forces acting on the weight into their components. The weight has a vertical component and a horizontal component. The vertical component is equal to the weight itself, which is 668 N downward. The horizontal component is zero since there is no force acting in the horizontal direction.

Next, let's analyze the forces acting on the weight due to the cables. The left-hand cable exerts a force T2, which can be resolved into vertical and horizontal components. The vertical component of T2 is T2 * sin(θ2) and acts upward, opposing the weight. The horizontal component is T2 * cos(θ2) and is balanced by an equal and opposite horizontal component from the right-hand cable.

The right-hand cable has a force of 550 N, making an angle of 45 degrees with the ceiling. We can resolve this force into vertical and horizontal components as well. The vertical component of 550 N force is 550 N * sin(45°) acting upward, opposing the weight. The horizontal component of the 550 N force is 550 N * cos(45°) acting to the right, balancing the horizontal component of the left-hand cable.

Since the net force in the horizontal direction is zero, the horizontal components from both cables must be equal and opposite:
T2 * cos(θ2) = 550 N * cos(45°)

Now, let's solve this equation for T2. Divide both sides of the equation by cos(θ2):
T2 = (550 N * cos(45°)) / cos(θ2)

The answer is T2 = (550 N * cos(45°)) / cos(θ2), where θ2 is the angle of the left-hand cable with respect to the wall.