Answer to Question #232784 in Physics for mar

Question

. A Christmas decoration consisting of three balls was hanged from the ceiling as shown in the figure. The tensions, TS, TE and Tm in the portion of the strings supporting the Christmas balls are 8N, 4N and 1N, respectively. Assume that the mass of the string can be neglected. Do the balls have the same mass? Support your answer by a mathematical solution

Answer 1

The balls have a different mass. According to Newton's first law, the system is in equilibrium when the resultant force (the sum of all forces) is zero. We have:

$$T_m=W_m=1\text N,\\ T_E=W_E+W_m=4\text N,\\ T_S=W_S+W_E+W_m=8\text N.$$

As we see from the first two equations, if the balls were of equal weight, T_E would be 2N, but it is 4. Similarly, T_S would be 6N, but it is 8.