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The two angled ropes used to support the crate in the figure below an withstand a maximum tension of 1300 N before they break. The left angle is 30dregres, and the right angle is 45degrees. What is the largest mass the ropes can support? m=?

  • physics -

    look at the horizonal (I assume the angles are measured to the horizontal).

    Tleft*cos30=Tr*cos45
    and the vertical..
    Tleft*sin30+Tr*cos45=mass*g

    so solve for Tleft in the first equation:
    tleft=Trcos45/cos30
    Trcos45/cos30 *sin30+Trcos45=mg
    solve for Tr. Put that in the equation for tleft. Then set it equal , 1300N
    thensolve for mass.

  • physics -

    is the answer 123.79 kg? or Newtons? thank you for the help

  • physics -

    it should be in kg.

  • physics -

    ..... isnt it Trcos45-Tleftcos30= 0

    Tr = Tleftcos30/cos45?

  • physics -

    170kg

  • physics -

    T1*sin(180-30) + T2*sin30=-Mg*sin270.
    1300*sin150 + 1300*sin30 = -Mg*sin270
    650 + 650 = Mg.
    Mg = 1300 N.
    M = 1300/9.8 = 132.7 kg.

  • physics -

    Correction:
    T1*sin(180-30) + T2*sin45 = -Mg*sin270.

    1300*sin150 + 1300*sin45 = Mg.
    650 + 919.2 = Mg.
    Mg = 1569.2 N.
    M = 1569.2/9.8 = 160 Kg.

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