Block sliding down an incline plane

In summary, the given figure shows that when the block slides down by x metres, the spring also gets stretched by x metres. This is because the force pulling the wire is along the slope. To prove this mathematically, two different coordinate systems can be used: one for the FBD of the horizontal spring and another for the sliding block. In both systems, the force acting on the spring is T, which increases as the angle of the slope increases until reaching the maximum value of mg at a 90 degree angle. Examples of this can be seen in the link provided.
  • #1
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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  • #2
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.
 
  • #3
anuttarasammyak said:
Yes, it does.
Any hint on how to arrive at that equality? Like a mathematical proof?
 
  • #4
You see in the figure, say x stretched the spring, same x the bock goes along the slope.
220206.jpg
 
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  • #5
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/

:)
 

1. How does the angle of the incline affect the speed of the block?

The angle of the incline has a direct impact on the speed of the block. The steeper the incline, the faster the block will accelerate due to the force of gravity. As the angle decreases, the speed of the block will also decrease.

2. What is the relationship between the mass of the block and its acceleration down the incline?

The mass of the block has an inverse relationship with its acceleration down the incline. This means that as the mass of the block increases, its acceleration will decrease. This is due to the force of gravity remaining constant while the mass increases, resulting in a smaller acceleration.

3. How does the coefficient of friction affect the motion of the block?

The coefficient of friction plays a crucial role in the motion of the block. It determines the amount of frictional force acting on the block as it slides down the incline. A higher coefficient of friction will result in a slower acceleration and a shorter distance traveled by the block.

4. What other factors besides angle and mass can affect the motion of the block?

Other factors that can affect the motion of the block include the surface of the incline, the surface of the block, and any external forces acting on the block. A rough surface will increase friction and slow down the block, while a smooth surface will decrease friction and increase the speed of the block.

5. How can we calculate the acceleration of the block down the incline?

The acceleration of the block can be calculated using the formula a = g(sinθ - μcosθ), where g is the acceleration due to gravity, θ is the angle of the incline, and μ is the coefficient of friction. This formula takes into account the forces acting on the block and can be used to determine its acceleration at any point down the incline.

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