Answer to Question #85210 in Mechanics | Relativity for Maria

Question

As shown in (Figure 1), five balls (masses m1 = 2.20kg, m2 = 2.15kg, m3 = 2.12 kg , m4 = 2.05 kg , m5 = 2.00kg) hang from a crossbar. Each mass is supported by "5-lb test" fishing line which will break when its tension force exceeds 22.2 N ( = 5.00 lb). When this device is placed in an elevator, which accelerates upward, only the lines attached to the 2.05 kg and 2.00kg masses do not break.
Within what range is the elevator's acceleration?

Answer 1

Newton's second law of motion is what you need. The lines break in case if tension in them is more than

$$T_\text{break}=m(g+a)>22.2\text{ N}.$$

According to this condition, the strongest broken line was that with $m_1=2.20$ kg. Therefore, the lowest acceleration required to break the heaviest mass was

$$a_1>\frac{22.2}{m_1}-g=\frac{22.2}{2.2}-9.8=0.29\text{ m/s}^2,$$

and the maximum acceleration was high enough to break the line with $m_3$ but not so high to break the line with $m_4$:

$$a_2\leqslant \frac{22.2}{m_4}-g=\frac{22.2}{2.05}-9.8=1.03\text{ m/s}^2.$$

The acceleration (in $\text{m/s}^2$) was within a range $0.29<a\leqslant1.03$.