Consider the 37 N weight held by two cables
shown below. The left-hand cable is horizontal.
a) What is the tension in the cable slanted
at an angle of 46◦?
Answer in units of N.
b) What is the tension in the horizontal cable?
Answer in units of N.
It matters where the 46 deg angle is.
Start with your basic laws:
TensionLeft*cosangleLeftToHorizontal=TensionRight*cosAngleRightToHoriz.
and
TensionL*sinAngleLeft+TensionR*sinAngleRight=weight
in all cases angles are measured to the horizontal.
solve for TensionL and TensionR
To find the tension in each cable, we can use the concept of equilibrium. In equilibrium, the net force and net torque acting on an object must be zero.
a) To find the tension in the cable slanted at an angle of 46 degrees, we'll start by resolving the forces acting on the weight along the horizontal and vertical axes.
Let's denote the tension in the horizontal cable as T_horizontal and the tension in the slanted cable as T_slanted.
Resolving the forces along the horizontal axis:
T_horizontal = 37 N (since the weight is balanced horizontally)
Resolving the forces along the vertical axis:
T_slanted * sin(46°) = 37 N (the weight is balanced vertically)
Now, we can solve for T_slanted:
T_slanted = 37 N / sin(46°)
b) To find the tension in the horizontal cable, we already found the value in part a, which is T_horizontal = 37 N.
Therefore,
a) The tension in the cable slanted at an angle of 46° is approximately T_slanted = 37 N / sin(46°) N.
b) The tension in the horizontal cable is T_horizontal = 37 N.