Question

A 650 N boy and a 490 N girl sit on a 150 N porch swing that is 1.70 m long. If the swing is supported by a chain at each end, what is the tension in each chain when the boy sits .75 m from one end and the girl .5 m from the other end?

Answer 1

The sum of the two chain tesnions is
T1 + T2 = 650 + 490 = 1140 N

Take moments about the chain nearest to the girl and set the sum equal to zero. Call the cable nearest the boy "1". The boy is 0.95 m from the girl's end, "2".

T1*1.7 -0.95*650 - 0.5*490 = 0

Solve for T1. Then use T1 + T2 = 1140 N to solve for T2.

Answer 2

Shouldn't we consider the weight of the swing as well?

Answer 3

Yes. Good thinking. I overlooked it

Answer 4

So then assuming the swing is uniform, do I have:

T1 + T2 = 650 + 490 + 150 = 1290 N

Then,

T1*1.7 -0.95*650 - 0.5*490 -.85*150 = 0

Solve for T1 and then use the first equation to solve for T2?

Answer 5

Yes. :-)

Answer 6

how is this equation right? when i multiplied all those numbers to get T1 i got a huge number...to plug it back in for T2 i would get a negative number...