Not sure if I have the correct angle and mass for this sum of forces

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SUMMARY

The discussion focuses on calculating the equilibrium of forces acting on a system involving weights and angles. The calculations yield two scenarios: one where the force E is determined to be 3.84 kg at an angle of 14.8º, and another where E is calculated as 7.6 kg at approximately 60º. The participants clarify the orientation of the plate and the distances of the masses from the origin, emphasizing the importance of understanding the forces acting on the system. The conversation concludes with a need for clarity on the vertical and horizontal balance of forces.

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dougiehazard
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Homework Statement
Balance the following face plate if the masses are as follows:A = 2.8 kg, B = 3.5 kg, C = 4.2 kg, D = 4.8 kg, E = ?(What angle and mass should E be placed to balance the other 4 masses
angle.PNG

Balance the forces east-west:

3.5kg*sin45º + 4.2kg*cos30º - 4.8kg*sin30º - E*cosΘ = 0

E*cosΘ = 3.712 kg
balance north-south:

2.8kg + 3.5kg*cos45º - 4.2kg*sin30º - 4.8kg*cos30º + E*sinΘ = 0

E*sinΘ = 0.982
EsinΘ / EcosΘ = 0.982 / 3.712

tanΘ = 0.2645

Θ = 14.8º ◄
E = 3.712kg / cos14.8º = 3.84 kg ◄
If that's not right, then you want to balance the moments.
balancing east west:

3.5kg*0.35*sin45º + 4.2kg*0.315*cos30º - 4.8kg*0.6*sin30º - E*0.2*cosΘ = 0

E*cosΘ = 2.86 kg
and north-south

2.8kg*0.35 + 3.5kg*0.35*cos45º - 4.2kg*0.315*sin30º - 4.8kg*0.6*cos30º + E*0.2*sinΘ = 0

E*sinΘ = 6.55 kg
EsinΘ / EcosΘ = 6.55 / 2.86

tanΘ = 1.706

Θ = 59.6º ≈ 60º
E = 6.55kg / sin59.6º = 7.6 kg
 
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I assume you are asking which approach is correct.
Are we to understand that the plate is mounted vertically on a horizontal axis through the origin, and that the numbers in the diagram are distances of the masses from the origin?
What forces act where?
 
forces are the weight id assume and yes the number are distances in the diagram
 
dougiehazard said:
forces are the weight id assume
Then why are you considering a horizontal balance of forces?
Does any other force act vertically?