An object whose mass is unknown is held by two rigid rods. The whole system is at rest. The angle between the vertical direction and the left rod from point A to B is 60 degrees. The angle between the vertical direction and the right rod from point C to D is 30 degrees. The forces in the rods are along the direction of the rods. It is known that the force in rod AB is 20 N. Another box, whose mass is 1.20kg is sitting ont he top of the unknown object through another rigid rod. What is the mass of the unknown object? Carefully draw the free body diagrams and show your calculations.
To find the mass of the unknown object, we can analyze the forces acting on it and the equilibrium conditions.
First, let's draw the free body diagram of the system:
```
A----------B
/ \
/ ? \
/ unknown object \
C-------------------D
|
1.20 kg
```
Now, let's label the forces acting on the system:
1. Force in rod AB (given): 20 N (upward)
2. Weight of the unknown object (mg): downward
3. Normal force on the unknown object (N1): upward
4. Force in rod CD (unknown): upward
5. Weight of the 1.20 kg box (m1g): downward
Since the system is at rest, the sum of the vertical forces must equal zero:
N1 - mg - m1g + 20 N = 0
We can then rearrange the equation to solve for the mass of the unknown object (m):
N1 - (m + m1)g = 0
m + m1 = N1 / g
Finally, substituting the given values: N1 = 20 N, m1 = 1.20 kg, and g ≈ 9.8 m/s²:
m + 1.20 kg = 20 N / 9.8 m/s²
m = (20 N / 9.8 m/s²) - 1.20 kg
m ≈ 1.8378 kg
Therefore, the mass of the unknown object is approximately 1.8378 kg.