Question III

III) The Figure below shows four penguins that are playfully pulled along very slippery (frictionless) ice by a curator. The masses of 3 penguins and the tension in two of the cords are given. Find the penguin mass that is not given (15 pts). Find the acceleration (5 pts).

Solution:
Let's look at the last two penguins. Then if we let the mass of the unknown penguin be m, we find that
111 N  =  (12 kg + m) a
and then looking at the whole system of four penguins,
222 N  =  (12 kg + m + 15 kg + 20 kg) a
where a is the acceleration of the four penguin system.
Then if we divide both equations, we find
$\frac{222}{111} = \frac{47 + m}{12 + m}$
or that
m = 23 kg
Now, we use that in the first equation to solve for the acceleration of the system and we find that
$a = \frac{111 N}{35 kg} ~=~ 3.2 m/s^{2}$