Spring and Rock Homework: Finding Separation

[Fontseeker]

Homework Statement

Homework Equations

U = (1/2)kx^2
T = 2 * π * (m/k)^ (1/2)

The Attempt at a Solution

[/B]
T = 2 * π * (m/k)^ (1/2)
T ^ 2 = 4 * π^2 * (m/k)
k = (4 * π^2 * m) / T^2

So I know the initial potential energy is:

U = (1/2)kx^2
U = (1/2)x^2 * ((4 * π^2 * m) / T^2)

However, I don't know how to find where the rock and the spring separate?

 

[tnich]

Homework Statement

View attachment 225095

Homework Equations

U = (1/2)kx^2
T = 2 * π * (m/k)^ (1/2)

The Attempt at a Solution

[/B]
T = 2 * π * (m/k)^ (1/2)
T ^ 2 = 4 * π^2 * (m/k)
k = (4 * π^2 * m) / T^2

So I know the initial potential energy is:

U = (1/2)kx^2
U = (1/2)x^2 * ((4 * π^2 * m) / T^2)

However, I don't know how to find where the rock and the spring separate?

There is a constant force of gravity acting on the rock. When happens when the acceleration of gravity is greater than the acceleration provided by the spring? What happens when it is less?

 

[Fontseeker]

There is a constant force of gravity acting on the rock. When happens when the acceleration of gravity is greater than the acceleration provided by the spring? What happens when it is less?

When the acceleration of gravity is greater than the spring, then they separate right?

 

[tnich]

When the acceleration of gravity is greater than the spring, then they separate right?

You are close, but that's not quite it. Will the rock separate when it is traveling downward, or upward?

 

[Fontseeker]

You are close, but that's not quite it. Will the rock separate when it is traveling downward, or upward?

The rock will separate as it is traveling upward, as soon as the spring stretches out (reaches its max amplitude), right?

 

[tnich]

The rock will separate as it is traveling upward, as soon as the spring stretches out (reaches its max amplitude), right?

Nope. Your were closer before. The separation point has to do with the acceleration.

 

[Fontseeker]

Nope. Your were closer before. The separation point has to do with the acceleration.

The spring will be acceleration up, and as long as the acceleration of the spring is greater than g, then so will the rock. As soon as the acceleration of the spring is less than g, it will separate right?

 

[tnich]

The spring will be acceleration up, and as long as the acceleration of the spring is greater than g, then so will the rock. As soon as the acceleration of the spring is less than g, it will separate right?

Right in a sense. You need to think about the signs of the accelerations.

 

[Fontseeker]

Right.

Now, I would just have to find the x at which the accelerations of both the spring and the rock equal the same using Newton's second law right?

 

[tnich]

Now, I would just have to find the x at which the accelerations of both the spring and the rock equal the same using Newton's second law right?

You were quick. I edited my answer. You still don't have it quite right. When the spring is accelerating upward and gravity is accelerating downward, the rock stay in contact. When the spring starts accelerating downward and it's acceleration downward is greater than the acceleration of gravity, then the rock will separate.
The question wants to know the amplitude at which the rock will separate. What equations do you know about simple harmonic motion that have acceleration and amplitude in them?

 

[Fontseeker]

You were quick. I edited my answer. You still don't have it quite right. When the spring is accelerating upward and gravity is accelerating downward, the rock stay in contact. When the spring starts accelerating downward and it's acceleration downward is greater than the acceleration of gravity, then the rock will separate.
The question wants to know the amplitude at which the rock will separate. What equations do you know about simple harmonic motion that have acceleration and amplitude in them?

I know a(t) = -Aw^2 * sin(wt). Now, I am trying to find when the acceleration starts accelerating downward, so I can just set to 0 right?

 

[jbriggs444]

I know a(t) = -Aw^2 * sin(wt). Now, I am trying to find when the acceleration starts accelerating downward, so I can just set to 0 right?

If you were holding a rock stationary on the palm of your hand, how fast would you have to accelerate your hand downward so that rock would fall freely?

 

[Fontseeker]

If you were holding a rock stationary in your hand, how fast would you have to accelerate your hand downward so that rock would fall freely?

I would have to accelerate it down at g.

 

[jbriggs444]

I would have to accelerate it down at g.

Right! So how fast does the block on which the fragment is resting have to accelerate downward so that the fragment falls free?

 

[Fontseeker]

Right! So how fast does the block on which the fragment is resting have to accelerate downward so that the fragment falls free?

I am not really understanding your question

 

[jbriggs444]

I am not really understanding your question

Replace your palm with a block. How fast does the block have to accelerate downward so that a rock sitting on top falls free?

 

[Fontseeker]

Replace your palm with a block. How fast does the block have to accelerate downward so that a rock sitting on top falls free?

It has to accelerate down at 9.8m/s^2

 

[jbriggs444]

It has to accelerate down at 9.8m/s^2

Right! Now all you have to do is figure out what amplitude of an oscillation results in the block having a downward 9.8 m/s^2 acceleration at some point.

 

[Fontseeker]

Right! Now all you have to do is figure out what amplitude of an oscillation results in the block having a downward 9.8 m/s^2 acceleration at some point.

I could use this equation, but I don't know w: a(t) = -Aw^2 * sin(wt)

 

[jbriggs444]

I could use this equation, but I don't know w: a(t) = -Aw^2 * sin(wt)

You know that the maximum downward acceleration occurs when sin(ωt) = what?

Edit: and you do know ω -- it is a function of f.

 

[Fontseeker]

You know that the maximum downward acceleration occurs when sin(ωt) = what?

Edit: and you do know ω -- it is a function of f.

sin(wt) = g / (Aw^2) right?

Would you find w using conservation of energy or how would you find it?

 

[jbriggs444]

Write omega in terms of f. The multiple choice answers you are given use f.

Edit: Also, answer the question: For a given amplitude A, the maximum downward acceleration of the block occurs when sin(ωt) = what?

 

[Fontseeker]

Write omega in terms of f. The multiple choice answers you are given use f.

Edit: Also, answer the question: For a given amplitude A, the maximum downward acceleration of the block occurs when sin(ωt) = what?

sin(wt) = g / (Aw^2) and then replace w using frequency right?

 

[jbriggs444]

sin(wt) = g / (Aw^2) and then replace w using frequency right?

Way easier than that.

The acceleration is maximum when sin(ωt) is maximum. What is the maximum value of sin(ωt)?