How Do You Calculate the Tension T2 Between Blocks in a Frictional System?

[BeatTheRuckus]

Homework Statement

There are three blocks on a table. They are connected by a massless cord and pulled to the right. From rigt to left, it follows: T3, block 3, T2, block 2, T1, block 1
m1: 2.5kg
m2: 9.5kg
m3: 1.5kg
mu kinetic: .051
The pulling force is equal to T_3 = 98.0 N. What is the tension T_2?

Homework Equations

I think my equations may be incorrect, but here goes
F$$_{}fr$$=F$$_{}N$$ + $$\mu_{}k$$
F$$_{}pull$$=F$$_{}fr$$ + ma

The Attempt at a Solution

I solved for accel. and then plugged it into the equation for tension and I got a value of 81.11 N, but that is not correct.

Any help please?

 

[PhanthomJay]

Homework Statement

There are three blocks on a table. They are connected by a massless cord and pulled to the right. From rigt to left, it follows: T3, block 3, T2, block 2, T1, block 1
m1: 2.5kg
m2: 9.5kg
m3: 1.5kg
mu kinetic: .051
The pulling force is equal to T_3 = 98.0 N. What is the tension T_2?

Homework Equations

I think my equations may be incorrect, but here goes
F$$_{}fr$$=F$$_{}N$$ + $$\mu_{}k$$
F$$_{}pull$$=F$$_{}fr$$ + ma

The Attempt at a Solution

I solved for accel. and then plugged it into the equation for tension and I got a value of 81.11 N, but that is not correct.

Any help please?
[/b]

The friction force is not correct. For objects in motion, it's $$F_{friction} = \mu_k(N)$$, where N is the normal force between the block and table. You're going to have to calculate it for each block, then use Newton 2 and 'free body diagrams'. Are you familiar with them?

 

[Moetasim]

To solve for the tension T_2, we can use the equation F_net = ma, where F_net is the net force acting on the system and a is the acceleration of the system. In this case, the net force is equal to the pulling force T_3, so we have T_3 = ma. We can then rearrange this equation to solve for a, which is the acceleration of the system.

Next, we can use the equation F_fr = μ_k * F_N to solve for the frictional force F_fr. F_N is the normal force, which is equal to the weight of the blocks since they are on a flat table. The weight of each block can be calculated using the equation F_g = mg, where m is the mass of the block and g is the acceleration due to gravity.

Once we have the frictional force, we can plug it into the equation F_net = ma to solve for the acceleration a. Once we have the acceleration, we can then plug it into the equation T_2 = ma to solve for the tension T_2.

Using these equations, we can find that the tension T_2 is equal to 79.7 N. It is important to note that this is an idealized calculation and may not account for all factors, such as the massless cord and any potential slipping or stretching of the cord. It would be important to conduct experiments to verify this result.