Centripetal Acceleration Lab Report
The point where the centripetal acceleration is provided completely by gravity is when the centripetal acceleration is equal to the gravity. This happens at the point where h=r/2.
As the truck moves from point A to point B, it would have decreased in height by r. Applying this again to our equation, we get;
Hence,
Using this in our g-force equation, we get;
And so the rider experiences an additional 2g of centripetal force from that experienced at the top.
Later, as the tuck moves to point C, the truck would have dropped a ∆h of 2r. This results in an additional acceleration of 4g from that at point A. Adding that to the acceleration at the top we get 5g, plus the g force already experienced by the body due to gravity we end …show more content…
The radius of the loop also changes as the graph progresses. This is exactly what we want in a roller coaster loop. We want the loop to start parallel to the straight track, and smoothly curve into a loop. We want the radius to slowly decrease over time until the radius at the top meets the radius of a circular loop.
To create a Clothoid loop we can join the graphs of two Clothoids:
Another way to get the desired shape of a roller coaster loop is by joining two identical circles where they overlap onto each other’s radii. By doing so, a third circle is formed in the middle with a smaller radius.
As we can see, we have created a loop with a small radius at the top and a large radius at the bottom. The small radius at the top allows the truck to maintain its acceleration since the speed is low, and the large radius at the bottom stops it from accelerating when the speed is high.
A Clothoid gives the ride a constant centripetal acceleration; however it does not provide a constant g-ride. This is because g force is proportional to the acceleration divided by gravity. Although both gravity and the centripetal acceleration, in this case, are constant, the direction is not. To better explain this we must provide an
As the truck moves from point A to point B, it would have decreased in height by r. Applying this again to our equation, we get;
Hence,
Using this in our g-force equation, we get;
And so the rider experiences an additional 2g of centripetal force from that experienced at the top.
Later, as the tuck moves to point C, the truck would have dropped a ∆h of 2r. This results in an additional acceleration of 4g from that at point A. Adding that to the acceleration at the top we get 5g, plus the g force already experienced by the body due to gravity we end …show more content…
The radius of the loop also changes as the graph progresses. This is exactly what we want in a roller coaster loop. We want the loop to start parallel to the straight track, and smoothly curve into a loop. We want the radius to slowly decrease over time until the radius at the top meets the radius of a circular loop.
To create a Clothoid loop we can join the graphs of two Clothoids:
Another way to get the desired shape of a roller coaster loop is by joining two identical circles where they overlap onto each other’s radii. By doing so, a third circle is formed in the middle with a smaller radius.
As we can see, we have created a loop with a small radius at the top and a large radius at the bottom. The small radius at the top allows the truck to maintain its acceleration since the speed is low, and the large radius at the bottom stops it from accelerating when the speed is high.
A Clothoid gives the ride a constant centripetal acceleration; however it does not provide a constant g-ride. This is because g force is proportional to the acceleration divided by gravity. Although both gravity and the centripetal acceleration, in this case, are constant, the direction is not. To better explain this we must provide an