How to solve this pendulum problem?

In summary: I'll try again.In summary, the three homework equations are:Centripetal force = m v^2/RT = centripetal force + wSigma F = m.a
  • #1
Helly123
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20

Homework Statement



For number 3,4,5
IMG_1092.png


IMG_1093.png


https://s4.postimg.org/qbp3xzq65/IMG_1092.png

https://s22.postimg.org/u220j60sx/IMG_1093.png

Homework Equations


Centripetal force = m v^2/R
T = centripetal force + w
Sigma F = m.a

The Attempt at a Solution


Number 3. Find the v at D point using mechanic energy eternity
While kinetic energy at A point is zero, and the potential energy is max (height max)
So, 1/2mvD^2 + mg.hD = 1/2mvA^2 + mg.hA
i don't know the height at D point...

After i find the v at D
I can find T
Which T = centripetal Force + weight
T = mvD^2/R + m.g

Number 4 almost the same
The string doesn't bend (what exactly it means...?)
So, centripetal force > weight??
m.vD^2/R > m.g ...(1)
But why the centripetal at point D has opposite direction than weight force? Is it because the string stuck at the nail at C point??

Find the v at D using mechanical energy eternity then add v to ...(1)

Number 5 i still don't know...
 

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  • #2
Hello Helly, :welcome:

Unfortunately your pictures don't show up in your post. I get:

upload_2017-6-8_13-33-27.png


Can you try again ?
 
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  • #3
BvU said:
Hello Helly, :welcome:

Unfortunately your pictures don't show up in your post. I get:

View attachment 205082

Can you try again ?
ok.. thanks for report. I've changed the pic.. :)
 
  • #4
Helly123 said:
So, 1/2mvD^2 + mg.hD = 1/2mvA^2 + mg.hA
with ##v_A = 0 ##.
i don't know the height at D point...
make a sketch of the situation and you know it. Note that CB = CD.
 
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  • #5
Helly123 said:
i don't know the height at D point
You know the length of the string, and you know how far C is below A. How far above C is D?
 
  • #6
is the height of D start from C or B ...?

CD = a-b
BC = a-b
if D start from C then height of D = a-b
if D start from B then height of D = 2(a-b)
 
  • #7
Check your energy conservation equation: If A is at height zero, you must take height of D wrt the same referernce.
 
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  • #8
Helly123 said:
is the height of D start from C or B ...?
BvU said:
Check your energy conservation equation: If A is at height zero, you must take height of D wrt the same referernce.
if A = height zero.. then kinetic energy is max...
then B point the kinetic energy is zero... how can it be...
 
  • #9
It was you who chose height A = 0 ! Therefore at point B the height is -a and the energy conservation still reads $$
{1\over 2} mv_B^2 + m g h_B = {1\over 2}mv_A^2 + mg\,h_A \quad {\rm or} \\
{1\over 2} mv_B^2 - mga = 0 $$
 
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  • #10
While kinetic energy at A point is zero, and the potential energy is max (height max)
BvU said:
It was you who chose height A = 0 ! Therefore at point B the height is -a and the energy conservation still reads $$
{1\over 2} mv_B^2 + m g h_B = {1\over 2}mv_A^2 + mg\,h_A \quad {\rm or} \\
{1\over 2} mv_B^2 - mga = 0 $$
BvU said:
It was you who chose height A = 0 ! Therefore at point B the height is -a and the energy conservation still reads $$
{1\over 2} mv_B^2 + m g h_B = {1\over 2}mv_A^2 + mg\,h_A \quad {\rm or} \\
{1\over 2} mv_B^2 - mga = 0 $$
hmm I see..
then it said the string doesn't bend, how that means Sir??
 
  • #11
As long as you have tension in a string, it does not bend but remains taut.
First work out number 3, once you have that, then number 4 is easy

By the way, what did you get for number 2 ?

Do you realize image 1093 is extremely fuzzy ?
 
  • #12
BvU said:
As long as you have tension in a string, it does not bend but remains taut.
First work out number 3, once you have that, then number 4 is easy

By the way, what did you get for number 2 ?

number 2? I get sqrt 2ga. do you even know the questions Sir.. but I'm still trying for number 3...
 
  • #13
Very unsharp, in image 1093 under (2) It says: Find the magnitude of the tension in the string just before the small ball reaches B.
##\sqrt{2ga}\ ## is not among the choices. But also, 2mg ...
Is the wrong answer (as I already suspected :rolleyes: ) .

You need to get this right: the same issue also needed in (3).
 
  • #14
BvU said:
Very unsharp, in image 1093 under (2) It says: Find the magnitude of the tension in the string just before the small ball reaches B.
##\sqrt{2ga}\ ## is not among the choices. But also, 2mg ...
Is the wrong answer (as I already suspected :rolleyes: ) .

You need to get this right: the same issue also needed in (3).
lol.. sorry Sir. I meant 3mg..
 
  • #15
Agree with 3mg.
 
  • #16
BvU said:
Agree with 3mg.
oh... it's my mistake... lol i'll try again number 3.. how do you even know the question for number 2, from the pic there's no number 2
 
  • #19
I know that.
 
  • #20
BvU said:
I know that.
I don't even understand... How to solve number 3...
 
  • #21
How to solve number 3...?
 
  • #22
At point D you know the speed from energy conservation.
So you know ##mv^2/r##.
Take gravity into account and then you have T.
 
  • #23
BvU said:
At point D you know the speed from energy conservation.
So you know ##mv^2/r##.
Take gravity into account and then you have T.
No the problem is idk the speed.. And not sure the height of D. If the string not bend, it's possible if only the string stuck at nail on C point then goes around to D, it means the height of D is a-b. The v^2 at D = 2gb.. Then.. I don't find the answer match the options
 
  • #24
Helly123 said:
it means the height of D is a-b
with respect to what reference point ?
Helly123 said:
The v^2 at D = 2gb
How do you calculate that ?
 
  • #25
BvU said:
with respect to what reference point ?
How do you calculate that ?
Do you know the answer already?
 
  • #26
Helly123 said:
Do you know the answer already?
Helly123 said:
Do you know the answer already?
CB = a-b
CD =CB
CD = a-b.
 
  • #27
Suppose a is 0.5 m and b is 0.4 m. What is the height of D ?
What is the formula for the height of D with your reference point O = 0 ?
 
  • #28
BvU said:
Suppose a is 0.5 m and b is 0.4 m. What is the height of D ?
What is the formula for the height of D with your reference point O = 0 ?
Since the ball goes around to D point, the reference i used no longer O=0 but C.. Cuz the T is at C.. No i used is at O the height is a (max)
 
  • #29
Helly123 said:
Since the ball goes around to D point, the reference i used no longer O=0 but C.. Cuz the T is at C.. No i used is at O the height is a (max)
we know that OC = b (0.4 m)
Then CB = a-b (0.5-0.4)m
Then CB = 0.1m
CD = 0.1m. Then use CD as height of D
 
  • #30
Can someone give me hint for number 5?
 
  • #31
Number 3 first. Write down clearly your energy conservation equation.
 
  • #33
Unconventional presentation, but (quite !) good. So, on to number (5):

##mv^2\over r## of tension is needed to maintain the circular motion.
Once the component of ##mg## along the wire exceeds ##mv^2\over r## the circular motion is interrupted. This happens somewhere between B and D, at a height above C.
Introduce some coordinate, e.g. ##\theta## and work out ##v(\theta)## and from that ##T(\theta)##.
 
  • #34
BvU said:
Unconventional presentation, but (quite !) good. So, on to number (5):

##mv^2\over r## of tension is needed to maintain the circular motion.
Once the component of ##mg## along the wire exceeds ##mv^2\over r## the circular motion is interrupted. This happens somewhere between B and D, at a height above C.
Introduce some coordinate, e.g. ##\theta## and work out ##v(\theta)## and from that ##T(\theta)##.
thanks Sir. that's the most effective way for me to fulfill your order. btw, on number 3-3 I set KE for D negative, because it goes to the left. is that ok??
 
  • #35
That's what I get for looking at the answers too summarily. Sorry.

No. Kinetic energy is never negative (*). The potential energy at D is not ##mg(2b-a)## but ##mg(a-2b)## because the height at D is lower than the height at A.

(*)
Both ##m## and ##v^2## are non-negative. For kinetic energy there is no direction, so 'because it goes to the left' does not apply.
 
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<h2>1. How do I calculate the period of a pendulum?</h2><p>The period of a pendulum can be calculated using the formula T = 2π√(L/g), where T is the period in seconds, L is the length of the pendulum in meters, and g is the acceleration due to gravity (9.8 m/s²). </p><h2>2. What is the formula for finding the velocity of a pendulum?</h2><p>The formula for finding the velocity of a pendulum is v = √(gL(1-cosθ)), where v is the velocity in meters per second, g is the acceleration due to gravity, L is the length of the pendulum, and θ is the angle of displacement from the vertical position.</p><h2>3. How do I determine the angle of displacement of a pendulum?</h2><p>The angle of displacement of a pendulum can be determined using the formula θ = sin⁻¹(a/L), where θ is the angle in radians, a is the horizontal displacement of the pendulum, and L is the length of the pendulum.</p><h2>4. What factors affect the period of a pendulum?</h2><p>The period of a pendulum is affected by the length of the pendulum, the acceleration due to gravity, and the angle of displacement. Other factors such as air resistance and the mass of the pendulum bob can also have a small effect on the period.</p><h2>5. How can I increase the period of a pendulum?</h2><p>To increase the period of a pendulum, you can increase the length of the pendulum or decrease the acceleration due to gravity. Additionally, reducing the angle of displacement can also increase the period of a pendulum. </p>

1. How do I calculate the period of a pendulum?

The period of a pendulum can be calculated using the formula T = 2π√(L/g), where T is the period in seconds, L is the length of the pendulum in meters, and g is the acceleration due to gravity (9.8 m/s²).

2. What is the formula for finding the velocity of a pendulum?

The formula for finding the velocity of a pendulum is v = √(gL(1-cosθ)), where v is the velocity in meters per second, g is the acceleration due to gravity, L is the length of the pendulum, and θ is the angle of displacement from the vertical position.

3. How do I determine the angle of displacement of a pendulum?

The angle of displacement of a pendulum can be determined using the formula θ = sin⁻¹(a/L), where θ is the angle in radians, a is the horizontal displacement of the pendulum, and L is the length of the pendulum.

4. What factors affect the period of a pendulum?

The period of a pendulum is affected by the length of the pendulum, the acceleration due to gravity, and the angle of displacement. Other factors such as air resistance and the mass of the pendulum bob can also have a small effect on the period.

5. How can I increase the period of a pendulum?

To increase the period of a pendulum, you can increase the length of the pendulum or decrease the acceleration due to gravity. Additionally, reducing the angle of displacement can also increase the period of a pendulum.

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