Question

Four penguins that are being playfully pulled along very slippery (frictionless) ice by a curator. The masses of three penguins and the tension in two of the cords are 1 12 m kg = , 3 15 m kg = , 4 20 m kg = , 2 111TN= , 4 222TN= . Find the penguin mass 2m that is not given.

Answer 1

`m_2 = 23 kg`

Step-by-step explanation:

As we know that the tension in two strings are

`T_2 = 111 N`

`T_4 = 222 N`

now we have

`F_(net) = ma`

so we can say

`(m_1 + m_2)a = T_2`

`(12 + m_2)a = 111`

also we have

`(m_1 + m_2 + m_3 + m_4) a = T_4`

`(12 + m_2 + 15 + 20) a = 222`

now divide two equations

`(222)/(111) = (47 + m_2)/(12 + m_2)`

`2m_2 + 24 = 47 + m_2`

`m_2 = 23 kg`