Bead on a string, find y(x) if horizontal velocity is const.

In summary, the conversation discusses a question about the conservation of energy in a system with changing height and constant horizontal velocity. The problem specifies that the horizontal velocity is constant, but not the vertical velocity or speed. The conversation also mentions using a physics principle to relate the total velocity at any point to the initial velocity.
  • #1
Phantoful
30
3

Homework Statement


5IgHXYY.png

Homework Equations


K = (1/2)mv2
U = mgh
W=Fd
Integration/Calculus

The Attempt at a Solution


I'm not sure what I should be doing for this question, if height changes how is it possible that velocity stays the same, according to the conservation of energy (frictionless wire)? If horizontal velocity stays the same, then I would assume that some sort of slope would equal 0 of this equation; however the line would be still at y=0, and it says there's an answer besides that. I'm not sure of any other weird functions that could do this, except maybe a circle (but I doubt that's the answer because it's a wire). How should I be solving this?
 

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  • #2
Note that the problem specifies that the horizontal velocity is constant at v0. There is no such constraint on the vertical velocity or the speed.
 
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  • #3
Also, given #2, how would you get the total velocity at any given point along the wire? How can you relate that to the initial velocity using some physics principle?
 
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1. What is the meaning of "bead on a string" in this context?

In this context, "bead on a string" refers to a simple physics problem where a bead is constrained to move along a horizontal line, or string, with a constant horizontal velocity.

2. What does "y(x)" represent in this problem?

"y(x)" represents the vertical position of the bead at a given time, where "x" represents the horizontal position. In other words, it is a mathematical function that describes the vertical displacement of the bead as it moves horizontally.

3. How is the horizontal velocity of the bead determined?

The problem states that the horizontal velocity is constant, meaning that it does not change over time. This velocity can be determined by measuring the distance the bead travels in a given time interval, and then dividing by the time interval.

4. What factors affect the vertical position of the bead in this problem?

In this problem, the vertical position of the bead is only affected by the initial vertical position and the acceleration due to gravity. Since the horizontal velocity is constant, it does not affect the vertical position of the bead.

5. How can the equation for y(x) be derived?

The equation for y(x) can be derived using the kinematic equations of motion, specifically the equation for displacement in the y-direction, which is y = y0 + vy0t + (1/2)at^2, where y0 is the initial vertical position, vy0 is the initial vertical velocity, t is time, and a is the acceleration due to gravity.

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