Consider the 59 N weight held by two cables The left-hand cable is horizontal.
What is the tension in the cable slanted
at an angle of 51◦? Answer in units of N.
What is the tension in the horizontal cable?
Answer in units of N.
see other.
To find the tension in the slanted cable, we can use trigonometry. Let's call the tension in the slanted cable T_slanted. Since the left-hand cable is horizontal, the tension in the left-hand cable will also be equal to T_slanted.
- To find T_slanted, we need to use the component of the gravitational force acting in the direction of the slanted cable.
- The weight is acting vertically downwards with a force of 59 N.
- We can find the component of the weight in the direction of the slanted cable by multiplying the weight by the cosine of the angle between the weight vector and the slanted cable.
- So, T_slanted = 59 N * cos(51°).
To find the tension in the horizontal cable, let's call it T_horizontal. Since the weight is held by two cables, the total vertical force (and therefore the tension in the vertical cable) must balance the weight of 59 N. The horizontal cable is perpendicular to the weight vector, so it does not contribute to balancing the weight vertically. Therefore, the tension in the horizontal cable will be equal to the component of the weight in the horizontal direction.
- The component of the weight in the horizontal direction can be found by multiplying the weight by the sine of the angle between the weight vector and the horizontal cable.
- So, T_horizontal = 59 N * sin(51°).
Calculating these values:
T_slanted = 59 N * cos(51°)
T_horizontal = 59 N * sin(51°)
Now, you just need to use a calculator to evaluate these expressions and obtain the values of T_slanted and T_horizontal in units of N.