1.6 Determine the maximum weight of the flowerpot that can be supported without exceeding a cable tension of 50 lb in either cable AB or AC. Note that the 2 cables make an angle 60 and 53.1 respectively with the horizontal

Let T1 and T2 be the two cable tensions. The vertical force applied by cable 1 is T1 sin 60 and the lateral force is -T1 cos 60. For cable 2 is is +T2cos 53 lateral and T2 sin 53 vertical.

Write equations of static equilibrium in each direction and then solve for the two unknowns in terms of the mass M. The more vertical cable T1 will probably have the larger tension. Determine the flowerpot weight (in lb) that makes T1 = 50 lb

thats my problem why does the more vertical cable have the larger tension

Determine the maximum weight of the flowerpot that can be supported without exceeding a cable tension of 50 Ib in either cable AB and AC.

To determine the maximum weight of the flowerpot that can be supported without exceeding a cable tension of 50 lb in either cable AB or AC, we need to analyze the tension forces acting on the cables.

Let's start by considering cable AB, which makes an angle of 60 degrees with the horizontal.

1. Identify the forces acting on cable AB:
- Tension force in cable AB (T_AB) pulling upward.
- Weight of the flowerpot (W) pulling downward.

2. Resolve the forces into their respective components:
- Tension force in cable AB (T_AB) can be broken down into two components:
- Tension force in the horizontal direction (T_AB_horizontal).
- Tension force in the vertical direction (T_AB_vertical).
- Weight of the flowerpot (W) can be broken down into two components:
- Weight in the horizontal direction (W_horizontal).
- Weight in the vertical direction (W_vertical).

3. Calculate the magnitude of the vertical component of the tension force (T_AB_vertical):
- Since cable AB makes an angle of 60 degrees with the horizontal, T_AB_vertical = T_AB * sin(60).

4. Calculate the magnitude of the horizontal component of the weight (W_horizontal):
- Since the weight pulls straight downward, W_horizontal = 0.

5. Calculate the magnitude of the vertical component of the weight (W_vertical):
- Since the weight pulls straight downward, W_vertical = W.

6. Set up the equilibrium equation in the vertical direction:
T_AB_vertical + W_vertical = 0.
This equation states that the sum of the vertical components of the forces must be zero, indicating that the forces are in equilibrium.

7. Solve for W (weight of the flowerpot):
- Substituting the values from step 3 and 5 into the equilibrium equation:
T_AB * sin(60) + W = 0.
- Rearrange the equation to isolate W:
W = -T_AB * sin(60).

8. Calculate the maximum weight that cable AB can support without exceeding a tension of 50lb:
- If we substitute the given maximum tension of 50lb into equation 7:
50 = -T_AB * sin(60).
- Solve for T_AB:
T_AB = -50 / sin(60).
- Plug the value of T_AB back into equation 7 to find the maximum weight:
W = -T_AB * sin(60).

Now, repeat the steps above for cable AC, which makes an angle of 53.1 degrees with the horizontal. This time, calculate Tension AC (T_AC) and substitute it into equation 7 to find the maximum weight that cable AC can support.

By following these steps, you can determine the maximum weight of the flowerpot that can be supported without exceeding a cable tension of 50lb in either cable AB or AC.