Newton's 2nd law with oscilations

[Danielpom]

Homework Statement

a car moving to the left with constent accelration. a ball is hanging from the ceiling held in 90 degrees to the ceiling until t=0, then it is realesed and start to swing.

find the max angle.

Homework Equations

Newton's second law

The Attempt at a Solution

gSin(α)-mCos(α)=A=R*(α'')

more detailed attempt

 

[PeroK]

You need to type out the key steps and your answer. Your attached notes are unreadable.

 

[Danielpom]

You need to type out the key steps and your answer. Your attached notes are unreadable.

thanks, fixed

 

[haruspex]

Homework Statement

a car moving to the left with constent accelration. a ball is hanging from the ceiling held in 90 degrees to the ceiling until t=0, then it is realesed and start to swing.

find the max angle.
View attachment 238653

Homework Equations

Newton's second law

The Attempt at a Solution

gSin(α)-mCos(α)=A=R*(α'')

View attachment 238660

more detailed attempt
View attachment 238658

I think you have confused yourself with regard to angles. Please define exactly what your angle α represents. What is its relationship to the given θ?

 

[Danielpom]

I think you have confused yourself with regard to angles. Please define exactly what your angle α represents. What is its relationship to the given θ?

θ is α. just called it by a different name...

 

[DrClaude]

Is the right answer supposed to be the one highlighted in yellow?

 

[haruspex]

θ is α. just called it by a different name...

That doesn't work. θ Is a given initial angle. You have a differential equation in which α is a variable.
You need to draw a diagram with the string at some intermediate position.

 

[Danielpom]

Is the right answer supposed to be the one highlighted in yellow?

yes

 

[DrClaude]

yes

In that case, I would appreciate some clarification about what the question is actually asking, "find the max angle." I suppose that the original is not in English but in Hebrew, but could you provide as close a translation as possible as to what is asked for.

 

[PeroK]

In that case, I would appreciate some clarification about what the question is actually asking, "find the max angle." I suppose that the original is not in English but in Hebrew, but could you provide as close a translation as possible as to what is asked for.

It's the maximum angle, not the equilibrium angle.

 

[PeroK]

yes

In any case, I suggest a major transformation would be helpful in tackling this problem. Have you ever heard of the equivalence principle?

 

[DrClaude]

It's the maximum angle, not the equilibrium angle.

I get that you and @haruspex understand the question better than I do! I'll stop asking for clarifications.

 

[Danielpom]

In any case, I suggest a major transformation would be helpful in tackling this problem. Have you ever heard of the equivalence principle?

didn't hear about it, do you have some info about it?

 

[Danielpom]

In that case, I would appreciate some clarification about what the question is actually asking, "find the max angle." I suppose that the original is not in English but in Hebrew, but could you provide as close a translation as possible as to what is asked for.

the angle θ until the time t=0 is 0 (the object is held in its place), then, at t=0 the object is released and start to oscillate. the acceleration of the car it's all happening at is ' a '. the question is, what will the maximum angle θ be during its oscillation.

 

[jbriggs444]

didn't hear about it, do you have some info about it?

The basic idea of the equivalence principle is that the effect of a gravitational field or of a uniformly accelerating platform are locally indistinguishable. Without looking out the window, there is no way to tell whether you are in an elevator accelerating upward in space or an elevator standing still on the ground floor.

Taking this a step farther, you can add up the effect of gravity plus the effect of a uniform acceleration and treat the vector sum as if it were pure gravity. One can justify this as follows:

1. Pretend that gravity is actually the whole lab experiencing 1 gee of vertical acceleration upward.
2. Add to that the constant leftward acceleration whose magnitude is a.
3. Determine the magnitude and direction of the resulting acceleration up and to the left.
4. Drop the acceleration and pretend instead that gravity has this magnitude and is acting down and to the right.

That is an efficient approach to this problem.

 

[Danielpom]

The basic idea of the equivalence principle is that the effect of a gravitational field or of a uniformly accelerating platform are locally indistinguishable. Without looking out the window, there is no way to tell whether you are in an elevator accelerating upward in space or an elevator standing still on the ground floor.

Taking this a step farther, you can add up the effect of gravity plus the effect of a uniform acceleration and treat the vector sum as if it were pure gravity. One can justify this as follows:

1. Pretend that gravity is actually the whole lab is experiencing 1 gee of vertical acceleration upward.
2. Add to that the constant leftward acceleration whose magnitude is a.
3. Determine the magnitude and direction of the resulting acceleration up and to the left.
4. Drop the acceleration and pretend instead that gravity has this magnitude and is acting down and to the right.

That is an efficient approach to this problem.

thank you very much for the detailed explenation! it is great. I'll try to think of it that way. Thanks.

 

[Danielpom]

The basic idea of the equivalence principle is that the effect of a gravitational field or of a uniformly accelerating platform are locally indistinguishable. Without looking out the window, there is no way to tell whether you are in an elevator accelerating upward in space or an elevator standing still on the ground floor.

Taking this a step farther, you can add up the effect of gravity plus the effect of a uniform acceleration and treat the vector sum as if it were pure gravity. One can justify this as follows:

1. Pretend that gravity is actually the whole lab experiencing 1 gee of vertical acceleration upward.
2. Add to that the constant leftward acceleration whose magnitude is a.
3. Determine the magnitude and direction of the resulting acceleration up and to the left.
4. Drop the acceleration and pretend instead that gravity has this magnitude and is acting down and to the right.

That is an efficient approach to this problem.

I tried looking at it your way, but didn't suceedto get the solution

 

[PeroK]

I tried looking at it your way, but didn't suceedto get the solution

How far did you get? Can you summarise your thinking?

Hint: this approach is so efficient that you hardly need any calculations. So, it's perhaps worth persevering with.