A roller coaster moving along its track rolls into a circular loop of radius r. In the loop, it is only affected by its initial

Question

3 months ago

7

A roller coaster moving along its track rolls into a circular loop of radius r. In the loop, it is only affected by its initial

velocity, gravity, and the shape of the track. Let v denote the instantaneous speed and a denote the magnitude of the instantaneous acceleration of the roller coaster in the loop. Which of the following is true in the loop?
a. The roller coaster is not in uniform circular motion, but we still have a=v^2/r everywhere on the loop
b. The roller coaster is not in uniform circular motion, but the tangential acceleration is so small that we can approximate a by v^2/r everywhere on the loop
c. The roller coaster is in uniform circular motion
d. The roller coaster is not in uniform circular motion, and a=v^2/r is only applicable at the very top and bottom of the loop where the tangential acceleration vanishes

Physics

2 answers:

Softa [3K] · Answer 1 · 2026-03-12T06:10:55+03:00

Softa [3K]3 months ago

5 0

Answer:

I'm quite sure it's the third option, but I might be mistaken

Explanation:

take care, 2021

Yuliya22 [3.3K] · Answer 2 · 2026-03-12T06:08:33+03:00

Answer:

c. The roller coaster maintains uniform circular motion

Explanation:

Since the loop is round with a radius r, its instantaneous speed, v, remains constant, and the centripetal acceleration can be expressed as a' = v²/r.

Because the angular speed, ω = v/r stays constant, although the direction of initial velocity changes, the size of its tangential acceleration equals zero. As a result, a" = rα and since Δω = 0, then α = 0 and a" = r(0) = 0

Consequently, no tangential acceleration is present. Since there’s no tangential acceleration, our overall instantaneous acceleration, which is the vector sum of centripetal acceleration and tangential acceleration, results in a = √(a'² + a"²) = √(a'² + 0²) = √a'² = a' = v²/r

Thus, a consistently equals v²/r.

Because the instantaneous acceleration remains as (a = v²/r) constant, the motion is categorized as uniform. Therefore, this is uniform circular motion.