Two identical springs with spring constant 50 N/m support a 5.0 N weight as in the picture below. What is the tension in spring A?
A)1.45 N
B)2.50 N
C)2.89 N
D)3.75 N
E)5.00 N

Question

Two identical springs with spring constant 50 N/m support a 5.0 N weight as in the picture below. What is the tension in spring A? 
A)1.45 N 
B)2.50 N 
C)2.89 N 
D)3.75 N 
E)5.00 N

Quizplus · Accepted Answer

Since the weight is supported by two identical springs, each spring has a tension of 2.5 N (half of the total weight of 5 N). 
However, spring A also experiences an additional force due to the compression of spring B. 
Assuming that the extension of both springs is x, the force exerted by spring B on spring A is kx, where k is the spring constant (50 N/m). 
Thus, the tension in spring A is 2.5 N + kx. 
Using Hooke's law, we know that the extension x is equal to the weight divided by the spring constant: x = 5 N / 50 N/m = 0.1 m. 
Therefore, the tension in spring A is 2.5 N + (50 N/m)(0.1 m) = 2.5 N + 5 N = 7.5 N. 
However, we need to remember that the tension in spring A has to be divided equally between the two segments of spring A due to the weight being located at the midpoint. 
Therefore, the tension in spring A is 7.5 N / 2 = 3.75 N.

Two Identical Springs with Spring Constant 50 N/m Support a 5.0