a store owner wishes to hang a sign weighinh 750N so that cable A attached to the store makes a 30 degree angle from the vertical wall. cable B is attached horizontally to an ajoining building. calculate the necessary tension on cable B
|.\
|30\
|...\ A
|....\
|.....\____B_____
so theres a triangle now with an inside angle of 120
saaw somewhere the answer is 433 but that's not what im getting
Physics - Damon, Saturday, November 17, 2012 at 8:28pm
T sin 30 = force up = 730
T = 1460 N in cable A
T cos 30 = horizontal component = 1460 cos 30 = 1264 N
I did not post this...Damon did
This problem
is the same thing but with a sign weighing 730 N
To calculate the necessary tension on cable B, we can use the concept of equilibrium. In equilibrium, the sum of all the forces acting on an object is zero.
In this case, we have two cables and the weight of the sign acting on the point of intersection. Let's denote the tension in cable A as T_A and the tension in cable B as T_B.
Now, let's break down the forces acting on the sign:
1. Weight of the sign (750N): This force acts vertically downwards. We can break it down into two components:
- Vertical component: 750N * sin(30°)
- Horizontal component: 750N * cos(30°)
2. Tension in cable A (T_A): This force acts along the direction of cable A.
3. Tension in cable B (T_B): This force acts along the direction of cable B.
Since the sign is in equilibrium, the sum of all these forces must be zero:
Sum of vertical forces = Sum of horizontal forces
Vertical forces:
- T_A * cos(30°) (acting upwards)
- 750N * sin(30°) (acting downwards)
Horizontal forces:
- T_A * sin(30°) (acting towards the left)
- T_B (acting towards the right)
- 750N * cos(30°) (acting towards the right)
Setting up the equations:
T_A * cos(30°) - 750N * sin(30°) = T_A * sin(30°) + T_B + 750N * cos(30°)
Now, solve the equation for T_B:
T_B = T_A * cos(30°) - 750N * sin(30°) - T_A * sin(30°) - 750N * cos(30°)
Simplifying the equation:
T_B = T_A * (cos(30°) - sin(30°)) - 750N * (sin(30°) + cos(30°))
Finally, we need to substitute the known values. T_A is not given, so we can't calculate the exact tension in cable B without that information. However, you can substitute the known values of sin(30°) and cos(30°) and solve for T_B if you have the value of T_A.