When an object is placed on a horizontal surface with no friction, the object will not start moving on its own. This is because according to Newton’s first law of motion, an object at rest will stay at rest unless acted upon by an unbalanced force. On a frictionless horizontal surface, there are no unbalanced forces acting on the object in the horizontal direction, so the object remains at rest.

## What causes an object to start moving on a frictionless surface?

For an object to start moving on a frictionless horizontal surface, an external force needs to be applied to it in the horizontal direction. This unbalanced force causes the object to accelerate in the direction of the applied force, as described by Newton’s second law of motion. Some examples of how an external force can make an object start moving on a frictionless surface are:

- Pushing or pulling the object with your hand
- Hitting the object with another object like a ball or hammer
- Applying a horizontal force via a string, spring, or compressed air
- Using gravity to pull the object down an inclined plane
- Applying electric or magnetic forces to create horizontal acceleration

As long as the external net force applied to the object has a horizontal component, the object will start accelerating horizontally on the frictionless surface as Newton’s second law dictates.

## What determines how fast an object will move on a frictionless surface?

According to Newton’s second law of motion, the acceleration of an object is directly proportional to the net force acting on it, and inversely proportional to its mass:

a = F_{net}/m

Where a is acceleration, F_{net} is net force, and m is mass.

This means that on a frictionless surface, the accelerating force applied to an object and its mass determine how fast it will move. A larger force will speed it up more quickly. A larger mass will slow the acceleration down. Some examples:

- A basketball and bowling ball are pushed with the same force. The basketball accelerates faster because it has less mass.
- A box is pushed gently at first, then more forcefully. It speeds up more as the force increases.
- Two carts with different masses are pulled along a frictionless track by identical springs. The less massive cart has greater acceleration.

In summary, the magnitude of the net force and the mass determine the acceleration and thus the speed of an object on a frictionless surface.

## What happens when the accelerating force is removed?

According to Newton’s first law of motion, an object will keep moving at the same velocity it was traveling at before the force on it was removed. This is because without any net external force, the object’s velocity will remain unchanged.

So if an object was accelerating along a frictionless horizontal surface due to an applied force, and then that force is removed entirely, the object will keep moving at the constant velocity it had the instant before the force disappeared. This velocity is called the final velocity of the object.

Without the accelerating force, the net force on the object becomes zero. So the acceleration becomes zero as well based on Newton’s second law. But the object does not immediately stop, it keeps coasting at the final velocity it reached when the force was removed.

This is an example of Newton’s first law – without a net force, an object’s motion does not change. The object remains in motion even after acceleration stops. It will keep coasting at that constant final velocity forever (neglecting other forces like gravity or air resistance).

## What is the effect of gravity on an object sliding horizontally?

When an object is sliding or rolling horizontally on a frictionless surface, the force of gravity acts on it in the vertical direction, not horizontally. So gravity does not directly affect the horizontal motion of the object.

However, gravity still has some indirect effects on the horizontal motion:

- It causes a normal force from the surface pushing upward on the object. This normal force can redirect some of the object’s vertical force into horizontal acceleration.
- It can cause the path of the object to curve downward into a parabolic trajectory due to the vertical acceleration of gravity.
- It can exchange vertical and horizontal velocity components when the object moves along an inclined plane or curved surface.

But if the frictionless surface is perfectly flat and horizontal, gravity does not directly apply any horizontal force or acceleration to an object moving across that surface. The horizontal motion remains unaffected.

## How is velocity affected when an object slides down an inclined plane?

When an object slides down an inclined plane with no friction, its velocity is affected in two main ways:

- The object accelerates vertically down the slope due to gravity. This increases its downward vertical velocity component over time.
- The downward vertical velocity gets converted into horizontal velocity due to the slope of the inclined plane. More specifically, the vertical velocity vector can be broken into components – one parallel to the surface and one perpendicular. The parallel component directly becomes horizontal velocity along the surface.

As a result, the total velocity of the object increases over time as it slides down the frictionless inclined plane. The total velocity has both a horizontal component parallel to the surface, and a vertical component down the slope. The horizontal velocity component increases as the object slides further down the incline.

The conversion of vertical to horizontal velocity obeys the kinematics equation:

v_{x} = v_{y} * sin(θ)

Where v_{x} is horizontal velocity, v_{y} is vertical velocity, and θ is the angle of inclination of the plane.

## What are some examples of objects sliding on frictionless surfaces?

Some common examples of objects sliding across low-friction or frictionless surfaces include:

- An air hockey puck gliding over an air hockey table
- An ice skater or hockey puck sliding across an ice rink
- A curling stone on a sheet of ice
- Bowling balls moving along bowling lanes
- Wheels, gears, and bearings in machines
- An object floating on a liquid surface like water or oil
- Spacecraft moving frictionlessly through the vacuum of space

These objects and systems exemplify very low amounts of kinetic friction that allows motion with constant velocity or minimal deceleration in the direction of motion. This makes them useful illustrations of Newton’s laws of motion.

## How can frictionless surfaces be created artificially?

There are several ways to reduce friction artificially in order to closely approximate a frictionless surface for experiments and demonstrations:

- Use a smooth level surface made of a very slippery material like glass, marble, or ultra-high molecular weight polyethylene plastic.
- Float an object on a liquid surface like water or oil. The fluid supports the object’s weight and reduces contact friction.
- Use an air cushion or air bearing that suspends the moving object on a thin film of air. Air hockey tables work this way.
- Levitate the object magnetically above the surface so no solid contact occurs. Maglev trains work this way.
- Chill a surface like a metal plate or block to cryogenic temperatures. This can reduce friction significantly.

While not perfectly frictionless, these methods can reduce friction enough to closely observe motion as if it were frictionless for experimental demonstrations and measurements.

## What factors affect friction on a horizontal surface?

Several factors can influence the amount of kinetic friction acting on an object sliding horizontally. These factors determine how closely the surface approximates being frictionless:

**Weight**– Heavier objects experience more friction.**Surface area**– More surface contact area produces more friction.**Surface smoothness**– Smoother surfaces have less friction.**Lubrication**– Oils, greases, or bearing surfaces reduce friction.**Surface material**– Materials like ice, Teflon, and metals have low friction.**Speed**– Faster motion can create more friction due to turbulence.**Temperature**– Extreme cold can reduce friction for some materials.**Wear and contaminants**– Dirt, scrapes, etc. increase friction over time.

By controlling these factors, horizontal friction can be reduced significantly. But attaining truly perfect zero friction is not possible except in superconducting systems.

## How is friction different when an object rolls instead of slides?

The friction forces are different when an object rolls horizontally instead of sliding. There are two major differences:

- Static friction provides the torque to make objects roll, so the static friction coefficient comes into play.
- Rolling objects experience less kinetic friction than sliding objects. The friction force depends on the radius of the rolling object.

For a rolling object, static friction between the surface and the bottom of the object provides the necessary torque to make the object rotate. Kinetic friction is reduced compared to sliding because only a tiny region of the object is sliding instantaneously at the point of contact.

The kinetic friction force for rolling is:

F_{f} = μk * F_{N} * (R / r)

Where μk is the kinetic friction coefficient, FN is the normal force, R is the radius of the rolling object, and r is the radius of the point of contact.

This means the friction force is reduced by a factor equal to the radius ratio R/r for rolling vs. sliding. So rolling objects can move much more easily across a horizontal surface.

## What happens if an external force is applied perpendicular to the motion of an object on a frictionless surface?

If a perpendicular external force is applied to an object moving horizontally on a frictionless surface, the object will begin accelerating perpendicularly without any change in its horizontal motion.

This is because based on Newton’s first law, the original horizontal velocity will remain unchanged in the absence of friction. At the same time, the new perpendicular force will cause perpendicular acceleration according to Newton’s second law.

The result is that with the perpendicular force applied, the object will begin moving in a curved trajectory, as it maintains its initial horizontal velocity while also accelerating perpendicularly.

For example, if a hockey puck sliding horizontally on ice has a force applied to its side, it will start curving sideways while maintaining its forward velocity. Or if a car were able to travel on a frictionless surface, pushing sideways on the car would start turning it without slowing the car’s forward motion.

The perpendicular change in motion will follow Newton’s equations, not interfering with the existing motion. After the perpendicular force is removed, the object will once again continue moving linearly along its original direction of travel.

## What path does an object follow if multiple forces act on it on a frictionless surface?

If multiple external forces act simultaneously on an object on a frictionless horizontal surface, the object will follow a resulting trajectory determined by vector addition of all the forces.

Specifically, the total net force can be calculated by adding together the vector components of each individual force. Then Newton’s second law is applied to this net force to determine the resulting acceleration at each instant.

Integrating the accelerations over time gives the trajectory followed by the object under the influence of the multiple forces. This trajectory is found by keeping a running vector sum of the velocity at each moment based on the calculated accelerations.

For example, if a horizontal force propels an object forward, while a downward gravitational force acts on it, the trajectory will be a parabolic arc. Or if horizontal and vertical forces act, the object may follow a diagonal linear path different from either force vector individually.

In general, when multiple perpendicular forces act on an object on a frictionless surface, the motion is a vector sum of the motions caused by each force independently. The object follows the net resultant trajectory determined by this vector addition.

## What happens when objects collide on a frictionless surface?

When objects collide on a frictionless horizontal surface, the total initial momentum of the system is conserved. Momentum is only transferred between objects, but is not lost due to friction.

After the collision, the velocities of the objects may change direction based on collision geometry and how the momentum is distributed. But the vector sum of momentums will be the same before and after the collision.

Additional outcomes of frictionless collisions:

- Kinetic energy is approximately conserved for elastic collisions.
- Some kinetic energy is converted to other forms like heat or sound in inelastic collisions.
- The center of mass of the system moves at constant velocity throughout the collision.
- Collisions can cause objects to start spinning if impact is off-center.

So on a frictionless surface, momentum is conserved while energy may or may not be lost depending on the type of collision. The collision’s geometric details determine the motion after the collision.

## How would a force or impulse applied to an object on a frictionless surface be represented in a physics engine simulation?

In a physics engine simulation that calculates object motions, forces and impulses applied to objects on frictionless surfaces can be represented through code and mathematics in a few ways:

- Directly set the velocity of the object to a new value when a force/impulse is applied.
- Numerically integrate the acceleration produced by the force/impulse using Newton’s law to obtain velocity changes over time.
- For impulses, directly add the impulse vector to the object’s momentum vector using the relationship: Impulse = Change in momentum.
- Track velocity vectors at each frame, adding any new perpendicular force/impulse vectors through vector addition.

The simulation can model frictionless behavior by not deducting any kinetic friction forces and allowing velocities to persist unchanged unless acted on by a force/impulse. Velocities can be tracked as 2D or 3D vector quantities and altered through vector equations.

For simplicity, directly setting velocities or modeling impulses through momentum changes works well. The engine should ensure changes only occur in the direction of the applied force/impulse by using vector math.

## How are Newton’s laws of motion for frictionless surfaces applied in the design of mechanical systems?

Engineers use Newton’s laws of motion for frictionless surfaces to inform the design of low-friction mechanical systems in several key ways:

- Predict motion and forces for frictionless models as an ideal starting point.
- Select materials and lubricants to approximate frictionless behavior in bearings, joints, etc.
- Model theoretical behavior of systems by neglecting friction as a first approximation.
- Calculate impulse/momentum changes from collisions in low-friction systems.
- Determine effects of gravity and inclines on sliding motion.
- Design guidance systems and controls for low-friction environments like space.

Frictionless conditions allow the clearest application of fundamental dynamics equations. So engineers use these idealized models, then incorporate appropriate friction factors when evaluating real-world systems.

## Conclusion

The motion of objects on frictionless horizontal surfaces provides insight into Newton’s laws in their simplest theoretical form. With no friction forces, objects continue moving at constant velocity unless acted on by external forces. The velocity changes depend directly on the net force and mass based on \\(\mathbf{F} = m\mathbf{a}\\). Gravity induces vertical motion but no horizontal acceleration unless the surface is inclined. Multiple forces result in trajectories found through vector addition. Conservation of momentum governs collisions. These fundamental physics principles for idealized frictionless motion establish the foundation for analyzing more complex real-world dynamics problems.