As shown in (Figure 1), five balls (masses m_1 = 2.20 kg, m_2 = 2. 15 kg,m_3 =2.

Question

As shown in (Figure 1), five balls (masses m_1 = 2.20 kg, m_2 = 2. 15 kg,m_3 =2.10 kg , m_4 = 2.04 kg , m_5 = 2.00 kg) 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 2.04 kg and 2.00 kg masses do not break. Within what range is the elevator's acceleration? Express your answers using two significant figures separated by a comma.

Explanation / Answer

using an equation, we have

m4 (g + a) > 22.2 N                          { causes the cord to break }

And

m3 (g + a) < 22.2 N                          { leaves the cord unbroken }

solving an above two eq. and we get

[(22.2 N) / (2.1 kg)] - g < a < [(22.2 N) / (2.05 kg)] - g

where, g = acceleration due to gravity = 10 m/s2

(10.5 m/s2) - (10 m/s2) < a < (10.8 m/s2) - (10 m/s2)

0.5 m/s2 < a < 0.8 m/s2

Now, a range of the elevator's acceleration which is given as :

amin = 0.5 m/s2           and            amax = 0.8 m/s2

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