a 9.0-kg model airplane is tied to the ceiling with two strings as shown below. What is the tension in each string?

Question

Answer 1

Assuming the plane is in equilibrium we need to resolve horizontally and vertically. Letting the tensions be T₁ and T₂ we have:

(→) T₁cos45 = T₂cos35...(1)

(↑)  T₁sin45 + T₂sin35 = 9g...(2)

(1) into (2) for T₁ gives:

(T₂cos35/cos45)sin45 + T₂sin35 = 9g

=> T₂cos35tan45 + T₂sin35 = 9g

i.e. T₂(cos35tan45 + sin35) = 9g

Hence, T₂ = 9g/(cos35tan45 + sin35)

so, T₂ = 63.3 N

Then, T₁ = (63.3)cos35/cos45

so, T₁ = 73.4 N

:)>

Answer 2

Solution: S₁= 73.37 N, S₂= 63.33 N

Remove the restraints and replace them with reactions in strings.

Left string - reaction S₁ up and left

Right string - reaction S₂ up and right

Balance of forces in the y-direction (up is +)

ΣY=0

S₁ sin 45° +  S₂ sin 35° - mg = 0 ........ (1)

Balance of forces in x-direction (right is +)

ΣX=0

-S₁ cos 45° + S₂ cos 35° = 0 ........ (2)

add these equations

S₁ (sin 45° - cos 45°) + S₂ (sin 35° + cos 35°) - mg = 0

sin 45° = cos 45° so the 1st term disappears

S₂ (sin 35° + cos 35°) = mg

S₂ = mg / (sin 35° + cos 35°)

S₂ = 9 * 9.8 / (sin 35° + cos 35°) = 63.33 N

From (2)

S₁ = S₂ cos 35° / cos 45°

S₁ = 63.33 cos 35° / cos 45° = 73.37 N

Use (1) to check the result

73.37 * sin 45° + 63.33 sin 35° - 9 * 9.8 = 0 

OK

Answer 3

   First to post  help.... Assuming the strings meet at the origin of our coordinate system [ the center of gravity of the model airplane ... kind of looks like they would meet ]..... and the forces are in equilibrium [ the plane is hanging perfectly still ]......

let  T1 = left string tension   T2 = right

vertical forces  must add up to 0  ...... total of upwards  forces  must add up to total of down forces...

T1*sin 45˚,  T2 sin 35˚ =   upwards  forces

downward  force = mg

******************************

Horiz  Forces must be =        

so total of all forces Rt. =  total of all forces left

Rt =  T2 cos 35˚     left  =  T1 cos 45˚

Find  either T1, or T2  from Horiz  forces...

e.g   maybe    T1 = 1.247 T2  [ it's  not, actually ]

and then replace T1 in the vertical force equation ,  and solve for  T2 .... then go back and figure out T1.

You do the work now..

Don't forget to choose a Best Answer...

Answer 4

Certainly could be wrong, but don't you need to know the center of gravity of the model?