Block sliding down an incline plane

Click For Summary

Discussion Overview

The discussion revolves around the mechanics of a block sliding down an inclined plane and its interaction with a spring. Participants explore the relationship between the distance the block slides and the extension of the spring, as well as the forces involved in the system.

Discussion Character

  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • Some participants assert that if the block slides down by x meters, the spring also stretches by x meters.
  • One participant requests a mathematical proof to support the assertion that the spring stretches by the same distance as the block slides.
  • Another participant explains that the pulley changes the direction of the tension force in the string connecting the spring and the block, suggesting the use of different coordinate systems for analyzing forces.
  • It is noted that the tension force T acting on the spring is equal to mgcos(θ), and that this force increases with the angle of the slope until it reaches mg at a 90-degree angle.

Areas of Agreement / Disagreement

Participants generally agree that the spring stretches by the same distance as the block slides, but there is a request for mathematical proof, indicating that the discussion is not fully resolved.

Contextual Notes

Participants have not provided a detailed mathematical framework for the relationship between the block's movement and the spring's extension, leaving some assumptions and steps unresolved.

VVS2000
Messages
150
Reaction score
17
TL;DR
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
 
Physics news on Phys.org
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
 
Reply
  • Like
Likes   Reactions: Lnewqban
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/

:)
 

Similar threads

Undergrad Free inclined plane and a block sliding on it
  • · Replies 13 ·
Replies
13
Views
3K
Undergrad How does a screw roll down an inclined plane?
  • · Replies 5 ·
Replies
5
Views
3K
High School Rotational Dynamics: Confused about the tension in this string pulling a mass up an incline
  • · Replies 2 ·
Replies
2
Views
2K
High School Beam on an inclined plane
  • · Replies 4 ·
Replies
4
Views
672
Undergrad Forces to move on the level versus up an inclined plane
  • · Replies 12 ·
Replies
12
Views
2K
Undergrad Lagrangian approach for the inclined plane
  • · Replies 21 ·
Replies
21
Views
4K
High School Determine forces acting on double inclined plane
  • · Replies 13 ·
Replies
13
Views
2K
High School Question about the role of mass in inclined planes
  • · Replies 5 ·
Replies
5
Views
2K
High School Normal force in case of inclined plane and banked turn
  • · Replies 3 ·
Replies
3
Views
2K
High School Rolling Without Slipping on an Inclined Plane
  • · Replies 5 ·
Replies
5
Views
3K