Question

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?

Answer 1

Answer:

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:

$U=mgh$

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:

$K=\frac{1}{2}mv^2$

(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.

Answer 2

Answer:

B) Using a metal ball instead of a rubber ball

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?

A) Moving the track to a higher location  

B) Using a metal ball instead of a rubber ball  

C) Covering the track with a strip of sandpaper  

D) Decreasing the height at which the ball is let go

Explanation:

The ball eventually stops moving because it loses energy to the track and surrounding air. This energy is lost as heat, which is produced by friction between the ball and the track. Using a metal ball instead of a rubber ball will reduce friction, making the model coaster more efficient because less energy is lost to the environment.