# if the same ball rolls down from three different length trackways with a 20degrees elevation, its acceleration on the short-length trackway is 1.08m/s^2;its acceleration on the medium-length trackway is 1.79m/s^2;and its acceleration on the long-length trackway is 1.52m/s^2.

how do the values of aS,aM, and aL compare and account for the results and any diffrences.

what do you mean by aS, aM, and aL ?

aS=the acceleration of the ball on short-length trackway
aM=the acceleration of the ball on medium-length trackway
aL=the acceleration of the ball on long-length trackway

Well, assume the ball is rolling. Friction will have a greater effect on the long track, as it operates for a longer distance. That accounts for the difference between the medium and long.

I cant explain the short length, it should be a higher value, in my thinking.

## To compare the values of aS, aM, and aL, we can first consider the effect of friction on the ball as it rolls down the trackways.

Friction is a force that opposes motion and can cause deceleration or acceleration depending on the direction. In this case, it is likely that the friction is acting in the opposite direction of the ball's motion, resulting in negative acceleration or deceleration.

When we analyze the situation, we can see that the ball experiences more friction as it rolls down the longer trackway compared to the shorter trackway. This is because the ball spends more time in contact with the track surface on the longer trackway, allowing more time for friction to influence its motion.

Therefore, it is expected that the acceleration on the long-length trackway (aL) is smaller than the acceleration on the medium-length trackway (aM) due to the greater effect of friction. This is consistent with the values given in the question, where aL = 1.52 m/s^2 and aM = 1.79 m/s^2.

However, the value of aS = 1.08 m/s^2 for the short-length trackway is lower than expected based on the reasoning above. This suggests that there may be other factors at play, such as differences in the smoothness or surface conditions of the trackways, which can affect the friction experienced by the ball.

To further understand the discrepancy for the short-length trackway, it would be helpful to consider additional information about the setup, trackway characteristics, or experimental conditions.