Does the Bead's Speed Change as It Slides Along a Frictionless Curve?

[member 198005]

Homework Statement

The figure below shows a bead sliding without friction along a curved wire in a vertical plane.
IMAGE: http://img545.imageshack.us/i/bead.png/

The bead slides starting from rest at position B on the frictionless wire. The direction of the gravitational field is in the -y direction (toward the bottom of the page).

I then have 6 statements that I have to determine if they are true, false, greater than, less than, or equal to:

1.) The acceleration in the x-direction at H is ... zero.
2.) The speed at C is ... the speed at A.
3.) The acceleration in the y-direction at H is ... zero.
4.) The acceleration at C is zero.
5.) The velocity at A equals the velocity at C.
6.) The speed at H is ... the speed at C.

Homework Equations

change KE + change PE = 0

The Attempt at a Solution

I feel confident for numbers 2, 5, and 6.

2 - Points C and A appear to be at the same height which means their PE is the same which means their KE are the same. Equal To

5 - While the speeds may be the same (for the same reason as 2) the velocity also takes into account the direction, which isn't the same in this case. False

6 - H is lower than C, which means there is a greater amount of potential energy at C. Greater Than

Now for 1, 3, and 4.

1 - It appears to be at the bottom of the curve. As the bead is descending the bead is gaining speed in the x direction, and as the the bead is ascending the bead is losing speed. It has to change signs at some point which means it has to equal zero at the bottom. Equal To

3 - The speed increases rapidly as the bead first falls and then tapers off until the speed downwards is zero. The acceleration must be towards the positive Y direction then? Greater Than

4 - In this case both accelerations (X and Y directions) must be taken into account. I believe the acceleration in the X direction is still zero because of the same line of reasoning as 1. Acceleration in the -Y direction should actually be increasing though. False

Is there anything wrong with my way of thinking? I just don't feel overly confident in my answers.

Thanks a bunch!

 

[member 198005]

The diagram is missing. :( or else I would have tried.
If you want somebody to explain it on a white-board, you can take live online help offered by www.myphysicsbuddy.ca[/URL]. I used the free demo given and they are good at such stuffs.
Let me know if it helps.
Cheers[/QUOTE]
The picture doesn't show up?

[ATTACH=full]140319[/ATTACH]

 

[member 198005]

Well I added the link to the picture. Hope that works. Thanks for your offer, but I'm too cheap to pay for help :P (I can see I get one free trial)

 

[member 198005]

Figured it out

 

[rwisz]

Your reasoning seems sound for the most part. Here are some comments and clarifications:

1) You are correct in that the x-component of acceleration is zero at the bottom of the curve, since the bead is moving with a constant speed horizontally. However, keep in mind that acceleration can also be in the negative direction, so you may want to specify that the acceleration is zero and positive at the bottom. Also, be careful with your terminology - acceleration is not speed, it is the rate of change of velocity with time.

2) Your reasoning is correct, but just to clarify, the speeds at C and A are equal because the bead is sliding along a curved path, which means its speed is constant. The fact that they are at the same height is not necessarily what makes their speeds equal.

3) Your reasoning is correct here as well. Since the bead is sliding along a curved path, it must have a component of acceleration in the y-direction in order to change its direction of motion. This acceleration is towards the positive y-direction at the bottom of the curve, and decreases as the bead moves up the curve until it reaches H, where it becomes zero. So the acceleration in the y-direction at H is greater than zero.

4) Your reasoning is correct - the bead is moving with a constant speed at C, so its acceleration must be zero. However, you may want to specify that this is the x-component of acceleration, since the bead does have a y-component of acceleration due to gravity.

5) Your reasoning is correct - the velocities at A and C are not equal because they have different directions.

6) Your reasoning is correct - the speed at H is less than the speed at C because the bead is moving uphill at H, so it has less kinetic energy (and therefore less speed) than at C where it is moving downhill.