A car is traveling at a constant speed along road ABCDE. (Curve BC where Bis beginning of curve and C is the end of the curve is in the shape of a "backward C." C is then the beginning of another curve and D is the end of the same curve in the shape of a normal C, like you are beginning to make an 8. Section AB and DE are straight.)
Rank the acceleration in each of the 4 sections (AB, BC, CD, DE) according to magnitude, listing the smallest first. Justity the rankings.
AB DE CD BC
To rank the acceleration in each section (AB, BC, CD, DE) according to magnitude, we need to consider the nature of the motion in each section.
1. Section AB: This section is straight, meaning the car is traveling in a straight line without any change in direction. Since there is no change in direction, the car's velocity remains constant, resulting in zero acceleration. Therefore, the acceleration in section AB is zero.
2. Section BC: This section is a curve in the shape of a "backward C." In this section, the car experiences a change in direction. When an object undergoes circular motion, it experiences centripetal acceleration. The magnitude of centripetal acceleration depends on the speed of the car and the radius of the curve. Generally, the acceleration in a curve is greater than zero but smaller than the acceleration in a straight line.
3. Section CD: This section is also a curve, but in the shape of a normal "C." Similar to section BC, the car undergoes circular motion and experiences centripetal acceleration. The magnitude of centripetal acceleration in section CD is the same as in section BC, assuming the radius and speed remain constant.
4. Section DE: Similar to section AB, this section is straight, meaning the car continues to travel in a straight line without any change in direction. Therefore, the acceleration in section DE is also zero.
Ranking the acceleration magnitude from smallest to largest:
AB (zero acceleration) < BC (centripetal acceleration) = CD (centripetal acceleration) < DE (zero acceleration)
Justification:
Section AB has zero acceleration because there is no change in velocity or direction. Sections BC and CD experience centripetal acceleration due to the change in direction, but their magnitudes are the same if the radius and speed remain constant. Section DE also has zero acceleration as there is no change in velocity or direction.
To rank the acceleration in each of the four sections (AB, BC, CD, DE), we need to consider the shape of the road and the characteristics of the car's motion.
First, let's define acceleration. Acceleration is the rate of change of velocity with respect to time. In simpler terms, it measures how quickly the car's speed is changing.
Section AB: Since section AB is described as a straight section of road, we can assume the car is traveling at a constant speed and direction. When the car's speed is constant, there is no change in velocity and therefore no acceleration. Therefore, the acceleration in section AB is zero.
Section BC: In Section BC, the road is described as a backward C curve. When a car is moving along a curve, it experiences centripetal acceleration, which is directed towards the center of the curve. In this case, the car is making a curve in the opposite direction of increasing values of the alphabet (backward C). The car's velocity is changing direction, and thus, it experiences acceleration. The magnitude of acceleration in section BC is positive and smaller compared to the next section.
Section CD: Section CD is also a curved section, but in the opposite direction of BC. The car is transitioning from the backward C curve to the normal C curve. Similarly to section BC, the car's velocity is changing direction, leading to acceleration. The magnitude of acceleration in section CD is larger compared to section BC because the car is transitioning from one curve to another.
Section DE: In section DE, the road is again described as a curve, but now it is a regular-shaped C curve, like you are beginning to make an 8. As in the previous sections, the car's velocity is changing direction, indicating acceleration. The magnitude of acceleration in section DE can be the largest since the car is moving along a continuous and more pronounced curve.
To summarize the rankings of acceleration from smallest to largest:
1. Section AB: The acceleration is zero since the car's speed remains constant.
2. Section BC: The acceleration is positive but smaller than the next sections since it is part of a backward C curve.
3. Section CD: The acceleration is larger than section BC as the car transitions from one curve to another.
4. Section DE: The acceleration can be the largest since it is a regular-shaped C curve.