How Do You Calculate Tension and Acceleration in a Pulley System?

[myoplex11]

Homework Statement

Determine the tension developed in the cords attached to each block and the accelerations of the blocks. Neglect the mass of the pulleys and cords. I have attached the picture below.

Homework Equations

Fnet=ma

The Attempt at a Solution

W=mg=(6*9.8)
I have no idea how to proceede any further

 

[tiny-tim]

… give the lengths names …

Hi myoplex11!

The first thing to do is to give the lengths of the cords letters, such as a and b.

I haven't seen the picture yet, so I don't even know if there's two blocks, but I assume a + b is a constant, so you can call that c, and then eliminate b by putting b = c - a.

Then you use your F = mx´´ equation to get an equation in a´´.

 

[Moetasim]

As a scientist, it is important to approach problems systematically and use the appropriate equations and principles to find a solution. In this case, we can use the concept of Newton's Second Law, F=ma, to solve for the tension in the cords and the accelerations of the blocks.

First, we need to draw a free body diagram for each block, considering all the forces acting on them. The forces acting on the top block are its weight (mg), the tension in the cord attached to it (T1), and the tension in the cord attached to the bottom block (T2). Similarly, the forces acting on the bottom block are its weight (mg), the tension in the cord attached to it (T2), and the normal force from the ground (N).

Next, we can apply Newton's Second Law to each block separately. For the top block, we have Fnet = ma, where Fnet is the net force acting on the block and a is its acceleration. We can write this as:

T1 - T2 = ma1

Similarly, for the bottom block, we have:

T2 - mg = ma2

Since both blocks are connected by the same cord, the tension in the cord (T2) will be the same for both blocks. We can use this fact to solve for T2 by substituting the value of T2 from the second equation into the first equation:

T1 - ma2 - mg = ma1

Now, we can solve for T1 by using the values of m, a1, and a2 from the given information. Once we have the value of T1, we can substitute it into the second equation to solve for T2.

Finally, we can use the values of T1 and T2 to solve for the accelerations of the blocks by rearranging the equations and solving for a1 and a2.

In conclusion, by using the principles of Newton's Second Law and drawing free body diagrams, we can solve for the tension in the cords and the accelerations of the blocks in this problem involving pulleys. It is important to approach problems systematically and use the appropriate equations and principles to find a solution.