Ball rolling down a segment then up a parabolic segment

In summary: I should have realized this before making a thread, but I didn't. In summary, the question asked for the maximum height the ball will reach on the right side after rolling down a straight segment and up a parabolic segment. Using energy conservation equations, it was determined that the ball will reach the same height as it started due to the deceptive nature of the additional information given in the question. This realization helps to better understand energy conservation principles.
  • #1
talaroue
303
0

Homework Statement


A 181 g ball is released from rest H=5.19 m above the bottom of the track shown in Figure. It rolls down a straight 21° segment, then back up a parabolic segment whose shape is given by y=x2/4, where x and y are in m. How high will the ball go on the right before reversing direction and rolling back down?
C10P81.jpg


Homework Equations


Ki+Ui=Kf+Uf
K=mv^2/2


The Attempt at a Solution


I am not sure how to start this because everytime i go to one direction i hit a dead end.
At the beginning it has both Ki=0 and Ui=0 correct?
Then at the final it has Kf and Uf right?
 
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  • #2
Here is my work but I don't even think I am on the right track...

This is for rolling down incline
Physics7.jpg



This is for rolling up the parabola
Physics8.jpg

EDIT: I put the wrong dominator in for the very last part when calculating Y it should be 4, but that anwser did not work either
 
  • #3
WOOOOOOW I am so sorry for wasting everyones times the parabola made me over think this equation since Ki+Ui=Kf+Kf...energy would force the ball up the same height as it began.
 
  • #4
The question gave you additional information to deceive you. Realizing this in the end only makes you understand energy conservation better. It's hardly wasting anyone's time.
 
  • #5
Yeah, I see what you mean but I didn't need to make a thread after.
 

1. What is the force causing the ball to roll down the segment and up the parabolic segment?

The force causing the ball to roll down the segment and up the parabolic segment is gravity. Gravity is a fundamental force of nature that causes objects with mass to be attracted to each other.

2. How does the shape of the segments affect the ball's motion?

The shape of the segments affects the ball's motion by changing the direction and speed of the ball. As the ball rolls down the segment, it gains speed due to the force of gravity. As it reaches the parabolic segment, the curvature of the shape causes the ball to change direction and move upwards, slowing down as it moves against the force of gravity.

3. What is the difference between rolling down a segment and up a parabolic segment?

The main difference between rolling down a segment and up a parabolic segment is the direction of motion and the forces acting on the ball. When rolling down a segment, the ball is accelerating due to the force of gravity. When moving up a parabolic segment, the ball is decelerating against the force of gravity.

4. How does the speed of the ball change as it moves along the segments?

The speed of the ball changes as it moves along the segments due to the forces acting on it. As the ball rolls down the segment, it gains speed due to the force of gravity. As it moves up the parabolic segment, the curvature of the shape causes the ball to slow down against the force of gravity.

5. What other factors can affect the ball's motion along the segments?

Other factors that can affect the ball's motion along the segments include the mass and size of the ball, the surface of the segments (friction), and any external forces acting on the ball (such as air resistance). These factors can impact the speed, direction, and overall motion of the ball as it rolls down the segment and up the parabolic segment.

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