How to find tension between the two blocks?

In summary, the problem involves two blocks of masses 12 kg and 18 kg connected by a massless rope and being dragged by a horizontal force of 68N. The coefficient of friction between each block and the surface is 0.10. By solving for the acceleration of the system and the tension in the rope, it is found that the acceleration is 1.28 m/s^2 and the tension is either the sum of the net forces on each block (3.6N and 5.4N) or the force required to overcome the frictional force of 29.4N.
  • #1
confused2009
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Homework Statement


Two blocks connected with a massless rope ,are being dragged by a horizontal force.suppose F= 68N, Mass1= 12 ,Mass2=18kg and coeffecient of fraction between each block and surface is 0.10.
12kg ------T--------18kg-----68N--->
Find tension and magnitude of the aceleration of the system


Homework Equations


f=mg, Fnet= Fa-ff, ff =mu *m*g


The Attempt at a Solution



Now I have tried to sovle it please see if this is correct or I need to change it----> 1st sloving for acceleration of the system Fnet=Ma
Fnet= Fa+Ff
Ff= (0.10)(9.8)(30)
force of friction= 29.4
so Fnet = 68N +(-29.4)
Fnet= 38.6N
acceleration= Fnet/mass
acceleration = 38.6/30= 1.28 m/s^2
This is probably the answer of the second question.
Now sloving for Tension
F=M_1a ( for 1st mass 12kg)
F= 12*1.28m/s^2
Force on 12kgmass= 15.36N
Force of friction 12kgmass= (12)(9.8)(0.10)= 11.76N
Net force on 12 kg mass= 15.36N+(-11.76)= 3.6N

F=M_2a (for 2nd mass18kg)
F= 18*1.28m/1.28m/s^2
Force on 18kg mass= 23.04
force of friction on 18kg mass=(18)(0.10)(9.8)=17.64
net force on 18 kg mass= 23.04N+(-17.64)= 5.4N

Now the net force on 12 kg mass is 3.6N and net force on 18 kg mass is 5.4N.
am I correct so far if yes , is the tension of the rope one of these values or the sum of these values , if one of these which one and why?
 
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  • #2
Welcome to PF.

You almost have it.

But the force of friction will add to the Tension not take away from it.

To accelerate the 12 kg block you must supply both the force to accelerate it at the system acceleration you found, as well as the force to overcome the retarding force of friction.
 
  • #3


Your solution for finding the acceleration of the system and the individual forces on each block is correct. However, in order to find the tension in the rope, we need to use Newton's second law, which states that the net force on an object is equal to its mass multiplied by its acceleration (F=ma). Therefore, to find the tension, we need to find the net force on the system and divide it by the mass of the system.

In this case, the net force on the system is the horizontal force of 68N, minus the force of friction on both blocks (29.4N). This gives us a net force of 38.6N. The mass of the system is the combined mass of the two blocks, which is 30kg. Therefore, the tension in the rope is 38.6N/30kg = 1.29N.

To answer your question about whether the tension is one of the individual forces or the sum of the forces, it is actually the sum of the forces. In this case, the tension in the rope is equal to the force on the 12kg mass (15.36N) plus the force on the 18kg mass (23.04N), which gives us a total of 38.4N. This is the same as the net force on the system, which we calculated earlier (38.6N).

In summary, to find the tension in the rope, we need to find the net force on the system and divide it by the mass of the system. This will give us the correct tension in the rope, which is the sum of the forces on each individual block.
 

FAQ: How to find tension between the two blocks?

1. How do you calculate tension between two blocks?

To calculate the tension between two blocks, you need to first determine the mass of each block and the angle of the rope or string connecting them. Next, you can use the equation T = m x g x sinθ, where T is the tension, m is the mass, g is the acceleration due to gravity, and θ is the angle of the rope or string. This will give you the magnitude of the tension force.

2. What factors affect the tension between two blocks?

The tension between two blocks can be affected by several factors, including the mass of each block, the angle of the rope or string, and the surface friction between the blocks and the surface they are resting on. In addition, any external forces acting on the blocks can also impact the tension.

3. How does the angle of the rope affect the tension between two blocks?

The angle of the rope or string connecting two blocks can significantly impact the tension between them. As the angle increases, the tension also increases. This is because a larger angle means a greater component of the weight of the blocks is acting in the direction of the rope, resulting in a higher tension force.

4. Can tension between two blocks ever be zero?

Yes, it is possible for the tension between two blocks to be zero. This can occur when the blocks are at rest on a horizontal surface with no external forces acting on them. In this case, the weight of the blocks is balanced by the normal force from the surface, resulting in zero tension in the rope connecting them.

5. How can tension between two blocks be used in real-world applications?

Tension between two blocks is an important concept in physics, and it can be applied in many real-world scenarios. Some examples include the use of tension in ropes or cables to lift heavy objects, in pulley systems to transfer motion and force, and in bridges and other structures to distribute weight and maintain stability. Understanding tension can also help in designing and building structures that can withstand various forces and loads.

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