Students design a model roller-coaster track. they place a rubber ball at the highest point on the track and let it go. the ball rolls along the track pulled only by the force of gravity. eventually, it comes to a stop. which change to the design will result in the ball moving the greatest distance?

Raising the highest point of the track to a higher point

Explanation:

When the rubber ball starts its motion, from the highest point of the track, it has only gravitational potential energy, given by:

where m is the mass of the ball, g is the gravitational acceleration and h is the height above the ground.

As the ball descends the track, this potential energy is partially converted into kinetic energy, given by:

(where m is the mass and v is the speed)

and partially lost as heat, due to the friction between the surface of the track.

As a consequence, the higher the initial height of the track (h in the formula), the greater will be the kinetic energy gained by the ball. A greater kinetic energy means a larger velocity, which also means that the ball will cover a longer distance before stopping.

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

                                              ⇒      

here   k is the proportionality constant whose value is 1.

                                                            [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.