# Solving for Pendulum Bob's d from Length L

• auk411
In summary: Yes, but you've put it on the wrong side of the equation.What matters is the difference in height, which is L - 2r, = L - 2(L - D). :wink:I'm still having trouble with the math. What is the difference in height? Is it the difference in the distance between the top of the bar and the bottom of the bar?I am confused about how to incorporate the radius of the smaller circle.In summary, the conversation involves a pendulum with a point-like bob swinging on a string with a fixed length attached to a pivot point. The bob is released from rest and swings to its lowest point where it makes contact with a horizontal bar positioned a distance d below the
auk411

## Homework Statement

Figure 2 shows a pendulum with a point-like pendulum bob on a string with a length = L fixedly attached to a support so as to form a friction-less pivot-point P. The bob is released at rest from the height of the pivot point. The bob swings to its lowest point where upon the string makes contact with a very thin horizontal bar positioned a distance d below the pivot point of the pendulum. The bob continues traveling past its lowest point with a new pivot point P’ and reduced radius of curvature and is barely able to travel to the top of the bar in a circular path. Find a very simple expression for d in terms of L.

see attachment

## Homework Equations

Work done by gravity = mgh

Radius of smaller circle = L -D

Fnet = T - mg = mv^2/r

## The Attempt at a Solution

?

someone at least show me how I'm supposed to be setting this up.

#### Attachments

• Figure 2.jpg
11 KB · Views: 311
welcome to pf!

hi auk411! welcome to pf!

hint: the tension at the end is zero, so if the speed at the bottom is v, what is the speed at the end?

tiny-tim said:
hi auk411! welcome to pf!

hint: the tension at the end is zero, so if the speed at the bottom is v, what is the speed at the end?

I get v^2 = g(L-D).

I then go on to say that mgL = .5m(v^2) - mg2(L-D).
= .5m(g)(L-D) - 2mg(L-D)
Reducing leads to L = .5(L-D) - 2 (L-D), which equals:
2L = L - D - 4(L-D).
2L = L -D -4L + 4D
2L = -3L + 3D
5L = 3D
(5/3)L=D

This is false. For D is shorter than L.

What gives?

I'm pretty sure the answer is D = (3/5)(L)

Also, I assume that y = 0 is directly below the starting position. So the y position of the first position of the bob is y = L.
B) No, I don't need help on the other thread. Thanks!

Last edited:
hi auk411!

(just go up :zzz: …)

(oh, and try using the X2 icon just above the Reply box )
auk411 said:
I then go on to say that mgL = .5m(v^2) - mg2(L-D).

ooh, your proof was fine, except that you screwed it up at the start with this line …

try it with a + instead of a -

tiny-tim said:
hi

ooh, your proof was fine, except that you screwed it up at the start with this line …

try it with a + instead of a -

Could you say WHY this is the case? I was under the impression that one of them had to be negative.

auk411 said:
Could you say WHY this is the case? I was under the impression that one of them had to be negative.

Yes, but you've put it on the wrong side of the equation.

What matters is the difference in height, which is L - 2r, = L - 2(L - D).

## 1. How do you calculate the displacement (d) of a pendulum bob from its length (L)?

The displacement (d) of a pendulum bob can be calculated using the formula d = L - L0, where L is the length of the pendulum and L0 is the length of the pendulum when at rest.

## 2. What is the significance of solving for Pendulum Bob's d from Length L?

Solving for the displacement (d) of a pendulum bob from its length (L) is important in understanding the motion of a pendulum. It allows us to calculate the amplitude of the pendulum's swing and determine the period of its oscillation.

## 3. How does the length (L) of a pendulum affect the displacement (d) of the bob?

The displacement (d) of a pendulum bob is directly proportional to its length (L). This means that as the length of the pendulum increases, the displacement also increases. This relationship is important in predicting the behavior of a pendulum.

## 4. Can the displacement (d) of a pendulum bob be negative?

Yes, the displacement (d) of a pendulum bob can be negative. This indicates that the bob is swinging in the opposite direction of its initial position. However, the magnitude of the displacement is always considered positive.

## 5. Are there any factors other than length (L) that can affect the displacement (d) of a pendulum bob?

Yes, there are other factors that can affect the displacement (d) of a pendulum bob, such as the angle at which the bob is released, air resistance, and the mass of the bob. These factors can alter the amplitude and period of the pendulum's oscillation.

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