Racing Balls
Find out a real time-saving shortcut.
What?
To demonstrate linear kinematics.
Two balls are launched at the same height on the end of two tracks with the same initial velocities. One ball travels on the straight track and the other on the track with a downhill. Which one reaches the other end of track first?
How?
Experimental Setup:
Two ball are set to roll on two separate tracks with the same initial and final horizontal level. One ball is to be released on a level track that gives no further acceleration while the other on a track with descending and ascending slopes.
- Put two identical balls at launchers that give the same initial velocity.
- Launch the balls, observe which one arrives at the end first.
×Experiments demonstration
Why?
When is the faster ball accelerated? Why is it accelerated?
×Think...
Since only the horizontal motion is considered, the vertical component of gravity can be neglected. The ball on the slant rail is subject to the normal force perpendicular to the rail surface, the horizontal component of this normal force accelerate the ball in the horizontal direction. The ball accelerate when it is sliding down.
Although the ball decelerates when rising up, but its velocity is still greater than the original horizontal velocity. Giving same horizontal distance for these two balls, the one with descending rail takes shorter time.
It may be easier with the v-t diagram (the relation between velocity v and time t). On the horizontal rail, the ball keeps the same velocity all the time, giving the initial velocity 
During the 
(on the diagrams, v is [horizontal component of the velocity])
Hence the area under the v-t curve represents the displacement, in our experiment the horizontal displacement is the same for these two rails (with different lengths). Compares fig. 1 with fig. 2, if the area 
Questions
- Does the two balls have the same terminal velocity?
- Does “arriving faster” means “getting energy from the outside” during the process? If so, where does this energy come from?
- What conditions does the time difference of these two balls depend on?
- Can the ball ascend no matter how deep it descends?
- What will the result be when considering the rotation of the balls?
- What will the result be when considering friction?
×Discussions
- Yes, since these two balls have equal mass and vertical displacement, there are equal amount of potential energy been transformed into kinetic energy, therefore they shall have the same terminal velocities.
- When the faster ball is passing through the downward rail, the difference of potential energy provides kinetic energy to make it moving faster.
- Depends on the area of the central bulge in the Fig. 2 v-t diagram. This portion represents the ball passing through the downward rail. So, the longer downward rail gives the greater time difference.
- Theoretically yes, giving the balls stay on the rails.
- Tip. In this case, part of the potential energy is transformed into rotational energy.
- Tip. In this case, the negative work of the friction force shall be taken into account.
About the Experiment
The horizontal and slant portions of the rail shall tangent to each other to keep the ball in contact with the rail surface.
Reference
- RACING BALLS (University of Maryland Physics Lecture-Demonstration Facility)
- Ching-Chi Chu (2008):從一個簡單的物理演示─「雙珠競走」看大一學生的力學概念。物理教育學刊,9(1), 137-150.
Producer
v.1 Ruei-Sing Jhou （周瑞星）
v.2 Mr. Zeng、永原儀器
Advisor
Tai-Sone Yih （易台生）, Tai-Li Chen （陳泰利）, Ching-Chi Chu （朱慶琪）
Written by
Tai-Li Chen （陳泰利）, Ching-Chi Chu （朱慶琪）
