How Do You Calculate the Mass of the Second Penguin?

[Angry Citizen]

Homework Statement

Four penguins are being playfully pulled along frictionless ice by a curator. The masses of three penguins and the tension in two of the cords are m1 = 12 kg, m3 = 15 kg, m4 = 20 kg, t2 = 111 N, and t4 = 222 N. Find the mass of the second penguin.

Note: t2 is the tension between the second penguin and the third penguin, and t4 is the tension between the curator and the fourth penguin.

Homework Equations

F=MA

The Attempt at a Solution

I don't know how to set up this problem. It is useless to separate it into its components using F=MA, since the acceleration is not given nor can it be derived without the second mass. I don't really understand the tension force very well since it runs counterintuitive to my sense of a free-body diagram. Can anyone clue me in on how to start?

 

[PhanthomJay]

Draw a free body diagram of the entire system: 'm2' and 'a' will be unknown variables. Then draw a free body digram of the first 2 penguins together: 'm2' and 'a' will be unknowmnvariables, and T1 won't matter in this FBD, because it is internal in this free body diagram. Solve the 2 equations for the 2 unknowns.

 

[Angry Citizen]

In the free body diagram, when drawing the tension force in t4, in which direction does it point? And all four penguins can be treated as a single 'particle' given that they move uniformly in the same direction, correct?

 

[PhanthomJay]

In the free body diagram, when drawing the tension force in t4, in which direction does it point? And all four penguins can be treated as a single 'particle' given that they move uniformly in the same direction, correct?

Yes, they can be treated as one large mass since they move together with the same speed ans acceleration and displacement. Tension "pulling" forces always pull away from the objects on which they act. Then you must isolate the penguins to determine the tensile forces in the rope.