a 9.0-kg model airplane is tied to the ceiling with two strings as shown below. What is the tension in each string?
- ?Lv 72 months ago
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
- SlowfingerLv 62 months ago
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 +)
S₁ sin 45° + S₂ sin 35° - mg = 0 ........ (1)
Balance of forces in x-direction (right is +)
-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
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
- MathguyLv 52 months ago
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...
- derframLv 72 months ago
Certainly could be wrong, but don't you need to know the center of gravity of the model?