Consider the 690 N weight held by two cables. The left-hand cable had tension T2 and makes an angle of 41◦ with the ceiling. The right-hand cable had tension T1 and makes an angle of 42◦ with the ceiling.
first figure the angles the verticalmakes with the cables.
Left=49
right:48
Sum of vertical forces is zero.
690-L*cos49 -R*cos48=0
put that into the form
a*L + b*R=c
then second equation: sum horizontal forces is zero.
L*sin49-R*sin48=0
so you have two equations, two unknowns, solve for L, and R
Thanks!
To solve this problem, we can use the principles of equilibrium which states that the sum of all forces acting on an object must be equal to zero.
Let's break down the weight force into its vertical and horizontal components.
1. Vertical Component:
The weight force is acting vertically downward. We can find its vertical component using the formula:
Weight vertical component = Weight × cos(angle with the ceiling)
Vertical component of weight = 690 N × cos(90°) = 0 N
2. Horizontal Component:
The weight force is acting horizontally. We can find its horizontal component using the formula:
Weight horizontal component = Weight × sin(angle with the ceiling)
Horizontal component of weight = 690 N × sin(90°) = 690 N
Now, let's analyze the tension forces in both cables.
For the left-hand cable:
The tension force (T2) has both vertical and horizontal components. We need to resolve it.
1. Vertical Component:
T2 vertical component = T2 × cos(angle with the ceiling)
Vertical component of T2 = T2 × cos(41°)
2. Horizontal Component:
T2 horizontal component = T2 × sin(angle with the ceiling)
Horizontal component of T2 = T2 × sin(41°)
Similarly, for the right-hand cable:
The tension force (T1) also has both vertical and horizontal components.
1. Vertical Component:
T1 vertical component = T1 × cos(angle with the ceiling)
Vertical component of T1 = T1 × cos(42°)
2. Horizontal Component:
T1 horizontal component = T1 × sin(angle with the ceiling)
Horizontal component of T1 = T1 × sin(42°)
Since the system is in equilibrium, the sum of the vertical components of the tension forces must balance the vertical component of the weight force.
Vertical component of T1 + Vertical component of T2 = Vertical component of weight
T1 × cos(42°) + T2 × cos(41°) = 0
Similarly, the sum of the horizontal components of the tension forces must balance the horizontal component of the weight force.
Horizontal component of T1 + Horizontal component of T2 = Horizontal component of weight
T1 × sin(42°) + T2 × sin(41°) = 690 N
These two equations can be used to solve for T1 and T2.
To find the tensions T1 and T2 in the cables, we can start by analyzing the forces acting on the weight.
Let's denote the weight as W = 690 N. We can break down this weight into its vertical and horizontal components.
The vertical component of the weight is Wv = W * sin(θ), where θ is the angle made by the cable with the ceiling. So, the vertical component of the weight is Wv = 690 * sin(90°) = 690 N.
The horizontal component of the weight is Wh = W * cos(θ). So, the horizontal component of the weight is Wh = 690 * cos(90°) = 0 N.
Next, we can analyze the forces acting on the weight in the vertical direction. Since the weight is in equilibrium, the total upward force should be equal to the total downward force.
The upward forces are given by the tensions T1 and T2, so the total upward force is T1*sin(θ1) + T2*sin(θ2).
The downward force is the vertical component of the weight, which is 690 N.
Therefore, we have the equation: T1*sin(θ1) + T2*sin(θ2) = 690 N.
Now, we need to analyze the forces acting on the weight in the horizontal direction. Again, since the weight is in equilibrium, the total leftward force should be equal to the total rightward force.
The leftward force is T1*cos(θ1), and the rightward force is T2*cos(θ2).
Therefore, we have the equation: T1*cos(θ1) = T2*cos(θ2).
To solve these two simultaneous equations, we need to know the values of θ1 and θ2.
Once you have the values of θ1 and θ2, you can plug them into the equations and solve for T1 and T2 using algebraic methods or a calculator.