Find tension in string between two blocks on horizontal surface

  • #1
I_Try_Math
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Homework Statement
Two blocks connected by a string are pulled across a horizontal surface by a force applied to one of the blocks, as shown below. The coefficient of kinetic friction between the blocks and the surface is 0.25. If each block has an acceleration of 2 m/s^2 to the right, what is the magnitude F of the applied force?
Relevant Equations
F = ma
1706249395888.png

IMG_20240126_010206.jpg

Did I draw the free body diagram incorrectly by treating the two blocks as one system? My textbook claims the answer is 25 N.
 
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  • #2
Your mistake is not exactly that you treat as one system but that you calculate the total normal force as equal to the total weight of the two bodies. Think again.

Hint : Each box has different normal force on it, in one it is equal to its weight but on the other it is NOT!!!
 
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  • #3
Delta2 said:
Your mistake is not exactly that you treat as one system but that you calculate the total normal force as equal to the total weight of the two bodies. Think again.

Hint : Each box has different normal force on it, in one it is equal to its weight but on the other it is NOT!!!
If I understand correctly, the magnitude of the larger block's normal force will be different than its weight which will change the friction calculation. Thank you very much for your help on this question, I'll redo the problem soon.
 
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  • #4
I_Try_Math said:
the magnitude of the larger block's normal force will be different than its weight which will change the friction calculation.
That's true, but for the purpose of answering the question in post #1 you can treat the two blocks as a unit. You just have to get the total normal force right.
Answering the question in the thread title is a different matter.
 
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  • #5
I_Try_Math said:
If I understand correctly, the magnitude of the larger block's normal force will be different than its weight which will change the friction calculation. Thank you very much for your help on this question, I'll redo the problem soon.
Yes. With a force of ##25N## at that angle, you might imagine that the first block is almost being pulled off the ground. It's a strange angle for the problem setter to choose.
 
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1. How do you calculate tension in a string between two blocks on a horizontal surface?

To calculate the tension in a string between two blocks on a horizontal surface, you can use the equation T = μ * (m1 * g + m2 * g), where T is the tension in the string, μ is the coefficient of friction between the blocks and the surface, m1 and m2 are the masses of the two blocks, and g is the acceleration due to gravity.

2. What factors affect the tension in the string between two blocks on a horizontal surface?

The tension in the string between two blocks on a horizontal surface is affected by the masses of the blocks, the coefficient of friction between the blocks and the surface, and the acceleration due to gravity. These factors determine the total force acting on the blocks and therefore the tension in the string.

3. Can the tension in the string between two blocks on a horizontal surface be greater than the weight of the blocks?

Yes, the tension in the string between two blocks on a horizontal surface can be greater than the weight of the blocks. This can happen if there is a force acting on the blocks in addition to gravity, such as a pushing or pulling force, which increases the total force acting on the blocks and therefore the tension in the string.

4. How does the angle of the string affect the tension between two blocks on a horizontal surface?

The angle of the string between two blocks on a horizontal surface can affect the tension in the string. As the angle of the string increases, the tension in the string also increases because the vertical component of the tension must counteract the weight of the blocks in addition to any horizontal forces acting on them.

5. What is the significance of finding the tension in the string between two blocks on a horizontal surface?

Finding the tension in the string between two blocks on a horizontal surface is important for understanding the forces acting on the blocks and ensuring that the system is in equilibrium. By calculating the tension, you can determine if the blocks are at rest or moving, and how much force is required to keep them in place. This information is crucial for designing and analyzing systems involving multiple objects connected by strings or ropes.

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