- #1
Kinetics of Masses on an Inclined Plane: Explaining Different Movements
- Thread starter darkmagic
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Discussion Overview
The discussion revolves around the dynamics of two blocks on an inclined plane connected by a pulley system. Participants explore the relationships between distance, velocity, and acceleration of the blocks, as well as the direction of their movements under various conditions.
Discussion Character
- Homework-related
- Conceptual clarification
- Technical explanation
Main Points Raised
- One participant questions why the 300lb block moves only half the distance of the 200lb block, suggesting that this affects both acceleration and velocity.
- Another participant explains that if the distance (x) is halved, then both velocity and acceleration are also halved, linking this to the mechanics of the pulley system.
- A participant challenges the assumption that the pulley moves only half the distance of the string, prompting further clarification.
- It is proposed that when the pulley moves down by a certain distance, it affects the length of the string on both sides, thus influencing the movement of the block on the slope.
- A participant expresses uncertainty about the direction of movement of the blocks and seeks guidance on how to determine this.
- Another participant suggests using force equations (F = ma) for each mass to analyze the situation, indicating that the heights of the masses need to be connected through a linear equation.
Areas of Agreement / Disagreement
Participants have not reached a consensus on the direction of movement of the blocks, and there are competing views on the mechanics of the pulley system and its effects on the blocks' motion.
Contextual Notes
Some assumptions regarding the mechanics of the pulley and the forces acting on the blocks remain unaddressed, and the discussion does not resolve the mathematical relationships needed to fully understand the system.
- #2
tiny-tim
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Hi darkmagic! 
velocity = dx/dt and acceleration = d2x/dt2, so if you halve x, you halve velocity and acceleration also.
(and of course x is halved because the pulley moves only half as far as the string)
velocity = dx/dt and acceleration = d2x/dt2, so if you halve x, you halve velocity and acceleration also.
(and of course x is halved because the pulley moves only half as far as the string)
- #3
darkmagic
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how can you know that the pulley moves only half of the string?
- #4
tiny-tim
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When the pulley goes down 1 cm, that makes the string above it 1 cm longer on both sides, which requires 2 cm of string, so the block on the slope moves 2cm.
- #5
- #6
tiny-tim
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Just ask yourself, does the pulley move? if it does, how many strings are attached? (because each string will have to get longer or shorter by the same distance)
- #7
darkmagic
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yes the blocks will move. my problem is in which direction will they move?
- #8
tiny-tim
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To find out, write the F = ma equations for each of the three masses.
(and, if the heights of the masses are x y and z, you'll need a linear equation connecting x y and z)
(and, if the heights of the masses are x y and z, you'll need a linear equation connecting x y and z)
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