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

AI Thread Summary
The discussion focuses on balancing forces in a system with various weights and angles. Two methods are presented for calculating the forces: one using direct force balance and the other involving moments. The calculations yield different values for the angle Θ and the force E, leading to confusion about which approach is correct. Participants clarify that the setup involves a plate mounted vertically, with distances from the origin representing the weights. The conversation raises questions about the necessity of considering horizontal force balance in the context of vertical forces acting on the system.
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?
 

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