Find tension in string between two blocks on horizontal surface

In summary, the task involves determining the tension in a string connecting two blocks resting on a horizontal surface. By analyzing the forces acting on each block, including gravitational force, friction, and any applied forces, one can apply Newton's second law to calculate the tension. This requires establishing free-body diagrams for both blocks and solving the resulting equations to find the tension in the string.
  • #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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FAQ: Find tension in string between two blocks on horizontal surface

How do you determine the tension in a string between two blocks on a horizontal surface?

To determine the tension in the string, you need to consider the forces acting on each block. Draw free-body diagrams for both blocks, apply Newton's second law (F = ma) to each block, and solve the resulting equations simultaneously. The tension will be one of the forces in these equations.

What role does friction play in calculating the tension between two blocks on a horizontal surface?

Friction can significantly affect the tension in the string. If there is friction between the blocks and the surface, you must include the frictional force in your free-body diagrams. The frictional force is calculated using the coefficient of friction and the normal force. This force opposes the motion of the blocks and alters the net force and acceleration.

How does the mass of the blocks affect the tension in the string?

The mass of the blocks directly affects the tension in the string. Heavier blocks require more force to accelerate, which increases the tension in the string. Conversely, lighter blocks require less force, resulting in lower tension. The masses of the blocks are used in the equations derived from Newton's second law to find the tension.

What is the effect of an external force applied to one of the blocks on the tension in the string?

An external force applied to one of the blocks will change the acceleration of the system and, consequently, the tension in the string. The direction and magnitude of the external force must be included in the free-body diagram and equations for the block to which it is applied. This force will contribute to the net force and affect the overall tension.

How do you handle a system with multiple strings and blocks on a horizontal surface?

For a system with multiple strings and blocks, you need to draw separate free-body diagrams for each block and write down the equations for each string's tension. Consider all forces acting on each block, including tension from multiple strings, friction, and any external forces. Solve the system of equations simultaneously to find the tensions in each string.

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