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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!
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