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=?
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.
it should be in kg.
..... isnt it Trcos45-Tleftcos30= 0
Tr = Tleftcos30/cos45?
170kg
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.
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.