If you have ever ridden on a chair lift at a ski area and had it stop, you know that the chair will pull down on the cable, dropping you down to a lower height then when the chair is in motion. The figure shows a gondola that is stopped. Find the magnitude of the tension in the cable toward each end of the cable if the total weight of the gondola and its occupants is 1,900 pounds. Apply the rules regarding the use of significant digits after all computations are complete. a = 71.6, b = 74.6
B)
C)
D)

Question

If you have ever ridden on a chair lift at a ski area and had it stop, you know that the chair will pull down on the cable, dropping you down to a lower height then when the chair is in motion. The figure shows a gondola that is stopped. Find the magnitude of the tension in the cable toward each end of the cable if the total weight of the gondola and its occupants is 1,900 pounds. Apply the rules regarding the use of significant digits after all computations are complete. ​a ​ = 71.6,  ​b ​ = 74.6 ​  ​
B)​ 
C)​ 
D)​

Quizplus · Accepted Answer

When the gondola is stopped, the tension in the cable towards each end of the cable will be unequal. Using the principle of static equilibrium, the tension towards each end of the cable can be found. 
Let T1 be the tension towards end A and T2 be the tension towards end B. 
∑Fy = 0 
T1 + T2 = mg 
∑Fx = 0 
T2a - T1b = 0 
where a and b are the distances from the center of gravity of the gondola to ends A and B respectively. 
Substituting a = 71.6 ft and b = 74.6 ft, and m = 1,900 lb, we get 
T1 = (T2b/a) = (950 lb)(74.6 ft/71.6 ft) = 986.78 lb 
T2 = mg - T1 = 1,900 lb - 986.78 lb = 913.22 lb 
Using the rules of significant digits, the final answer should have the same number of significant digits as the input values. Therefore, the tension towards each end of the cable is 
T1 = 987 lb and T2 = 913 lb, 
which corresponds to choice B.

If You Have Ever Ridden on a Chair Lift at a Ski