EK Physics 1001 #280

[nwdmd]

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Mass is supported by two strings.. angles are 60deg(left string), 30deg(right).

Find T2


Answer: 50N, system is in equilibrium, thus horizontal forces are equal: t1cos60 = t2cos30
and vertical forces are equal: mg=t1sin60 + t2sin30.

I understand conceptually that T1 would be larger (as angle increases cos decreases, so T increases (aka supporting a larger portion of the weight in the Y-plane). But how would one quickly solve for the actual tension? I'm sure I've been missing something simple 🙂


Keywords for future searches: EK exam krackers 1001 physics 280

 

[loveoforganic]

Total force in vertical direction - 100 N.

T1*sin60 + T2*sin30 = 100

T1*cos60 = T2*cos30

T2 = T1*cos60 / cos30 = T1 / sqrt 3

T1*sin60 + T1*sin30 / sqrt 3 = T1*(sin60 + sin30 / sqrt 3) = 100

T1 = 86.6

86.6*cos60 = T2*cos30

T2 = 86.6*cos60 / cos30 = 50.


That's the actual math. I can't remember all the neat little math tricks 🙁

 

[GRod18]

does anyone have anything not mathy for this problem? Although I guess thats probably was EK's intention, being mathy with tons of trigs.. lol

 

[Rabolisk]

The key is realizing that horizontally, all forces cancel out, and vertically they add to 100N . Conceptually T1 > T2 and T1 + T2 > 100. But that's about all I can say. Don't be afraid to do math. It's not even tough, as long as you know the sin/cos of common angles.

 

[GRod18]

The key is realizing that horizontally, all forces cancel out, and vertically they add to 100N . Conceptually T1 > T2 and T1 + T2 > 100. But that's about all I can say. Don't be afraid to do math. It's not even tough, as long as you know the sin/cos of common angles.

Thank you again!