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

Attachment image

1 Answer

Relevance
  • NCS
    Lv 7
    6 months ago
    Favorite Answer

    Welcome to Yahoo!Answers.

    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

    If you find this helpful, please select Favorite Answer. You get points too!

Still have questions? Get your answers by asking now.