# Kinematics of an Object Sliding along Terrain

• Ironfroggy
In summary, the conversation discusses the kinematics of an object sliding along a changing surface, such as an inclined plane or a ramp. It is mentioned that in the case of an inclined plane, the object's motion is affected by the projection of gravity on the plane. However, when the surface changes shape, the object's path of motion adheres to the shape of the surface. This is due to an elastic collision between the object and the surface, which keeps the object's velocity tangential to the surface. When the surface slopes down, the object may jump off if it is going fast enough, but the simulation shows that it will start bouncing and never stop. The scenario of a penguin or skier sliding on ice is used as
Ironfroggy
Hello,

I need help understanding the kinematics of an object sliding along a surface (not just a plane, but a changing surface), as I cannot find any information on this topic. Let's assume I have an object on a frictionless smooth continuous/differentiable surface in the field of gravity and that energy is conserved.

If this surface is just an inclined plane, then the motion of the object is described simply by the projection of gravity on the plane. However, what if the slope then smoothly inclines upward? Experience tells us that the object's path of motion will adhere to the shape of the surface and furthermore the shape does not affect |v| (only g*h does).

This cannot be described in terms of gravity/normal forces, so I assume the reason this happen is that an elastic collision occurs between the object and the surface and since the object's velocity was originally tangential to the surface, the reflected velocity will remain tangential (as long as the surface is differentiable).

The question now becomes what happens if the surface slopes down. In the case of a ramp, experience tells me if an object is going sufficiently fast it will simply jump off the surface and become a projectile. If it is not going fast enough, it will remain on the surface.

However, the math in this case would show that no matter the speed of the object, at the moment the path slopes down, it will have an upward velocity component and leave the path. Since the object is no longer tangential to the path, upon re-entry, it will start bouncing and this is what I get when I try to write a simulation: the object will at first nicely slide up/down a path, make the predicted jump and then start to bounce and never stop bouncing.

The scenario I'm looking to emulate is the classic one of the penguin/skier sliding on ice. The skier should jump off the surface when going sufficiently fast at an incline and return to the surface after doing a jump.

It is obvious that collision with the surface is not elastic in this case as the skier does not bounce, but then the velocity component along the surface should be attenuated likewise and motion would be short lived when the path changes shape. What's going on here? Also, there's the related problem of a wheel rolling on a surface with infinite friction.

The wheel should stick to the surface and not slip, but the simulation I wrote shows the wheel slipping instead; how can I model this behavior?Thanks in advance for your help.</code>

## 1. What is kinematics?

Kinematics is the branch of mechanics that studies the motion of objects without considering the forces that cause the motion.

## 2. What factors affect the kinematics of an object sliding along terrain?

The factors that affect the kinematics of an object sliding along terrain include the object's mass, the surface characteristics of the terrain, and the initial velocity of the object.

## 3. How is the velocity of an object sliding along terrain calculated?

The velocity of an object sliding along terrain can be calculated using the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.

## 4. What is the difference between translational and rotational motion in kinematics?

Translational motion refers to an object's change in position in a straight line, while rotational motion refers to an object's change in position around an axis. In the context of an object sliding along terrain, translational motion would be the object's movement along the surface, while rotational motion would refer to any spinning or rolling motion.

## 5. How do friction and gravity affect the kinematics of an object sliding along terrain?

Friction and gravity play significant roles in the kinematics of an object sliding along terrain. Friction acts in the opposite direction of the object's motion, slowing it down, while gravity pulls the object downwards, causing it to accelerate. Both of these forces must be taken into account when calculating the kinematics of an object sliding along terrain.

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