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.

 

[rwisz]

As a scientist, the first step in solving this problem would be to understand the concept of tension force. Tension force is a force that is transmitted through a string, rope, or cable when it is pulled tight by forces acting from opposite ends. In this case, the tension forces t2 and t4 are acting on the second and fourth penguins respectively, as they are being pulled by the curator.

To solve this problem, we can use the concept of Newton's second law, which states that the net force acting on an object is equal to its mass multiplied by its acceleration (F=ma). In this case, we can assume that the penguins are moving with a constant velocity, which means that the net force acting on them is zero.

Now, we can set up two equations using Newton's second law for the second and fourth penguins:

For the second penguin: t2 - m2a = 0
For the fourth penguin: t4 - m4a = 0

Since we know the values of t2, t4, and m4, we can solve for the unknown mass m2 by rearranging the equations:

m2 = t2/a
m2 = t4/a

Since both equations are equal to m2, we can set them equal to each other and solve for a:

t2/a = t4/a
t2 = t4
111 N = 222 N

This means that the tension forces t2 and t4 are equal, which also means that the acceleration of the penguins must be zero. This is consistent with our assumption that the penguins are moving with a constant velocity.

So, to find the mass of the second penguin, we can substitute the value of t2 into one of the equations and solve for m2:

m2 = t2/a
m2 = 111 N/0
m2 = 0 kg

This means that the mass of the second penguin is zero, which is not physically possible. This could indicate that there is missing information or a mistake in the given values.

In conclusion, to solve this problem we used the concept of tension force and Newton's second law to set up equations and solve for the unknown mass of the second penguin. However, the result of a mass of zero suggests that there may be missing information or a mistake in the given values. Further clarification or additional information would be needed to accurately solve this problem