Pendulum swings into a peg

In summary, the problem asks for the equation for the angle θ between the peg and the horizon when the string is at its lowest point. There is no mention of friction or force so it is unclear what equation would be needed.
  • #1

Homework Statement


With this problem I have to get the answer: cosθ = r/L * cosα - √(3)/2 * (1 - r/L)
which in other words mean I need to find angle θ with arccos[r/L * cosα - √(3)/2 * (1 - r/L)].

Here's the picture:
11d636180c.jpg

Lcosθ is the vertical length of the string at its lowest point.

rcosα is a fraction of that same vertical string in terms of displacement "r" (which is from the start of the string to the peg)

∠β is the angle between the peg and the horizon.

(L-r) sinβ is the height from the end of the peg and the horizontal

(L-r) cosα is the horizontal length of that same peg.

(L-r)cosα is the vertical length of the string from the ball to the peg.

So, this is not really a physics issue but more like a math issue but since this is a physics problem I've decided to put it under here.

My problem is that I am unable to continue from this point as shown on the picture of my attempt. I don't know where to continue from here on out. I am trying to find "t" for the equation but I am unsure how. Where do I continue from now?

Homework Equations


[/B]
Newtonian Position Formula:
yf = yi +viyt + .5gt2
xf = xi +vixt + .5gt2

Energy Equation:
Work of hand - force of friction * displacement = delta Kinetic Energy + delta Potential Energy

Wh - fF*d = [.5*mvf2 - .5*mvi2] - [mghf - mghi]

The Attempt at a Solution


Picture of Attempt:
e4bfe92db3.jpg
[/B]
 
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  • #2
Hello Stranger, :welcome:

Your position formula is only valid for uniform acceleration. You don't have that here !
Can you think of a condition you can impose on ##\beta## ?
 
  • #3
BvU said:
Hello Stranger, :welcome:

Your position formula is only valid for uniform acceleration. You don't have that here !
Can you think of a condition you can impose on ##\beta## ?

Thanks for the welcome :).
The only method I can think of when dealing with changing acceleration by breaking it into parts. Each part for every time the value of acceleration changes. I have not yet learned ho to derive very well but I know it exists. As for angle β I am clueless on what to impose.
 
  • #4
Well, then perhaps you can conquer this one without dealing with changing acceleration ?
The sketch suggests a trajectory, but is it realistic ? Where must the mass run out of sped to fall on the peg ? What would happen if it ran out of speed at e.g. 85 degrees ?
 

What is a pendulum?

A pendulum is a weight suspended from a fixed point so that it can swing freely back and forth under the influence of gravity.

What is a peg?

A peg is a small cylindrical or tapered piece of wood, metal, or plastic used to fasten or as an axis for a rotating object.

How does a pendulum swing into a peg?

A pendulum can swing into a peg when the peg is positioned in the pendulum's path and the pendulum's motion causes it to make contact with the peg.

What factors affect a pendulum's swing into a peg?

The factors that can affect a pendulum's swing into a peg include the length of the pendulum, the angle of release, the weight of the pendulum, and the height of the peg.

What applications does the concept of a pendulum swinging into a peg have?

The concept of a pendulum swinging into a peg has applications in various fields such as physics, engineering, and amusement park rides. It can also be used as a visual demonstration of the laws of motion and gravity.

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