dan asked in Science & MathematicsPhysics · 6 months ago

# 5: Balance the following face plate if the masses are as follows:A2.8kgB3.5kgC4.2kgD4.8kgE = ?

5: 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 masse

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• NCS
Lv 7
6 months ago

You have only one unknown. Do you want to balance the forces, or balance the moments? To do the latter, it assumes the face plate is horizontal and the masses are hanging over the edge.

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