Exploring the Relationship Between Incline Angles and Speed of a Rolling Ball

In summary, the problem involves comparing the speed of a ball rolling down three inclined planes with angles of 30, 45, and 60 degrees. The only variables that affect the speed are gravity and height, which are constant in all three scenarios. Therefore, the ball will reach the same speed at the bottom of each inclined plane, assuming there is no slipping or bouncing.
  • #1
nvez
21
0
[RESOLVED] Speed in relation to angles

Homework Statement


You leave a ball roll down 3 different inclined plans with the same height. They each have 30, 45 & 60 degrees of incline respectively. Compare the sped of each of these plans

Height = constant, doesn't change
Angles of plans = 30, 45, 60

Homework Equations


None that I know of.

The Attempt at a Solution


I honestly do not see a way how to resolve this problem, if anyone can just shed any light, I know we're working in energy at the moment but I cannot find a way to get information with just an angle.
 
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  • #2
That would be correct. Potential energy at the top will be kinetic energy at the bottom.

They will take different times to reach the bottom ... but at the bottom they will be going at the same speed. (Assuming there is no slipping at the steeper angle or bouncing on impact at the bottom etc.)
 
  • #3
I _think_ I got it, this is what I did

[tex]mgh = 1/2mv^{2}[/tex]

m = m therefore removed.

[tex]gh = 1/2v^{2}[/tex]

take 1/2 on other side becomes 2

[tex]2gh = v^{2}[/tex]

take the ^2 and make it sqrt the other side

[tex]\sqrt{2gh} = v[/tex]

Therefore we conclude that the only variables that matter in it's speed is the gravity and height, which is the same in all 3 problems therefore it will arrive at the same speed because gravity and height are constant?

Thanks in advanced if I'm correct. :)
 
  • #4
That's correct.
 
  • #5
LowlyPion said:
That's correct.

Thank you very much again, I really appreciate it! :)
 

FAQ: Exploring the Relationship Between Incline Angles and Speed of a Rolling Ball

What is the relationship between speed and angle?

The relationship between speed and angle is that as the angle increases, the speed also increases. This is because a larger angle means a longer distance to travel, which requires a higher speed to cover the same distance in the same amount of time.

How does changing the angle affect the speed of an object?

Changing the angle can greatly affect the speed of an object. As the angle increases, the speed also increases. However, if the angle is too steep, the object may lose speed or even come to a stop due to the increase in gravitational force.

Why is speed important in relation to angles?

Speed is important in relation to angles because it determines the distance an object can travel in a given amount of time. A higher speed allows an object to cover a larger distance in the same amount of time, while a lower speed means a shorter distance covered.

Can an object maintain the same speed while traveling at different angles?

No, an object cannot maintain the same speed while traveling at different angles. As the angle increases, the speed also increases in order to cover the longer distance in the same amount of time.

How does friction affect speed in relation to angles?

Friction can greatly affect the speed of an object in relation to angles. As the angle increases, the force of friction also increases, which can slow down the object and decrease its speed. This is why objects traveling on steeper angles tend to slow down or come to a stop due to the increased friction.

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