Consider a 648 N weight held by two cables.
The left-hand cable had tension T2 and makes
an angle of 53 degree with the ceiling.
The right-hand cable had tension T1 and
makes an angle of 40? with the ceiling.
a) What is the tension in the cable labeled
T1 slanted at an angle of 40? ?
Answer in units of N
b) What is the tension in the cable labeled T2
slanted at an angle of 53??
The horizontal components of the two tension vectors must be equal (and opposite) for the system to be in equilibrium.
cos(40) / cos(53) = 1.2728
So, we know the ratio of the two tensions, but we do not yet know the actual values.
We know that the sum of the vertical components must add up to 645 Newtons.
The tension of T2 will be
648 / [sin(40) + sin(53) * 1.2728] =390.528 N
The tension of T1 will be
390.528 * 1.0119 = 497.064 N