I Block sliding down an incline plane

AI Thread Summary
When a block slides down an inclined plane, it stretches the spring by the same distance, x meters. The direction of the force acting on the spring aligns with the slope due to the pulley system, which only changes the tension's direction. By establishing two coordinate systems—one for the horizontal spring and another for the inclined block—it's possible to analyze the forces acting on each. The tension force, T, remains consistent across both systems, equating to mgcos(θ). As the slope's angle increases, the tension force acting on the spring rises, reaching its maximum at a 90-degree angle.
VVS2000
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TL;DR Summary
In the given figure, if the block slides down by some x metres, does the spring also get strecthed by x metres? Or will it get strecthed due to the horizontal component of the force acting on the sliding block? Hence the expansion in the spring is caused due to the horizontal component of the force
20220206_112548.jpg
 
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VVS2000 said:
Summary:: In the given figure, if the block slides down by some x metres, does the spring also get strecthed by x metres?
Yes, it does. And the direction of the force pulling the wire is along the slope.
 
anuttarasammyak said:
Yes, it does.
Any hint on how to arrive at that equality? Like a mathematical proof?
 
You see in the figure, say x stretched the spring, same x the bock goes along the slope.
220206.jpg
 
That pulley only changes the direction of the tension force in the string or rope that connects the spring and the sliding block.

Because of that, you can create two different coordinate x-y systems: one for the FBD of the horizontal spring, in which the x-axis is horizontal and aligned with it, and another for the sliding block, in which the x-y system is inclined, being the x-axis aligned with the slope.

For each FBD, you will have a force T of the same magnitude (mgcos<).
If the angle of the slope increases, the value of force T acting on the spring also increases, until reaching the maximum value of mg at angle 90 degrees.

Please, see examples that are shown in this link:
https://courses.lumenlearning.com/suny-osuniversityphysics/chapter/5-7-drawing-free-body-diagrams/

:)
 
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