Calculating Tension in Rope of Accelerating Balloon

AI Thread Summary
The discussion focuses on calculating the tension in two ropes supporting a balloon that accelerates upwards at 0.40 m/s². For the first rope, with a mass of 15 kg, the gravitational force is calculated as 147 N, leading to a tension of -141.0 N, indicating a downward force. For the second rope, with a mass of 9 kg, the gravitational force is 88.2 N, resulting in a tension of -84.6 N, also indicating a downward force. The negative values suggest that the calculations may need reevaluation, as tension should be a positive value in this context. The participants seek confirmation on the accuracy of these tension calculations.
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Homework Statement


If the balloon in the diagram drawn below is accelerating upwards at 0.40 m/s2, calculate the tension in each piece of rope. Assume that the rope has no mass.
http://img261.imageshack.us/img261/964/capture2gm.png
http://img261.imageshack.us/img261/964/capture2gm.png


Homework Equations


a=0.40m/s^2
m=15kg
g=9.8m/s^2
F_t=?
F_g=?


The Attempt at a Solution


Rope 1

Step1
If the balloon in the diagram drawn below is accelerating upwards at 0.40 m/s2, calculate the tension in each piece of rope. Assume that the rope has no mass.





















Rope 1
a=0.40m/s^2
m=15kg
g=9.80m/s^2
F_t=?
F_g=?
Step1
F_g=mg
F_g=15*9.8
F_g=147m/s^2
Step2
Fnet=m*a
Fnet=F_g+F_t
15*0.40=147+F_t
6=147+F_t
6-147=F_t
-141.0N=F_t
Rope 2
a=0.40m/s^2
m=9kg
g=9.80m/s^2
F_t=?
F_g=?




Step1
F_g=mg
F_g=9*9.8
F_g=88.2m/s^2
Step2
Fnet=m*a
Fnet=F_g+F_t
9*0.40=188.2+F_t
3.6=88.2+F_t
3.6-88.2=F_t
-84.6N=F_t

Therefore the tension on rope 1 is -141.0N
Therefore the tension on rope 2 is -84.6N
 
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