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Problem 5. Carousel that's turning A carousel has two lanes of horses: an outer lane of radius 5.36 m and an inner lane of radius 3.78 m. When a ride starts, the carousel immediately starts rotating with some initial angular speed wo, and undergoes a constant angular acceleration a until it reaches its maximum angular speed, after which it rotates constantly at this angular speed. The carousel completes its first revolution in 23.0 s, then completes its second revolution after an additional 21.0s. At its maximum speed, the carousel completes one revolution every 14.0 s. During the ride, the horses also move up and down, and their vertical motion is independent of the angular speed of the carousel. The vertical displacement of each horse follows that of simple harmonic motion, with one up-and-down cycle lasting 3.50 s, and the height difference between each horse's highest point and lowest point being 20.3 cm. All horses start at their lowest point at the beginning of the ride. (a) Find angular acceleration a and initial angular speed wo of the carousel, and find the time at which the carousel reaches its maximum angular speed. (b) At t = 1.00 min, t = 2.00 min, and t = 3.00 min after the beginning of the ride, draw the velocity and acceleration vectors of a horse in the outer lane and a horse in the inner lane, with clearly labeled components. (If needed for clarity, you may draw both a top view and a side view.)

Problem 5. Carousel that's turning A carousel has two lanes of horses: an outer lane of radius 5.36 m and an inner lane of radius 3.78 m. When a ride starts, the carousel immediately starts rotating with some initial angular speed wo, and undergoes a constant angular acceleration a until it reaches its maximum angular speed, after which it rotates constantly at this angular speed. The carousel completes its first revolution in 23.0 s, then completes its second revolution after an additional 21.0s. At its maximum speed, the carousel completes one revolution every 14.0 s. During the ride, the horses also move up and down, and their vertical motion is independent of the angular speed of the carousel. The vertical displacement of each horse follows that of simple harmonic motion, with one up-and-down cycle lasting 3.50 s, and the height difference between each horse's highest point and lowest point being 20.3 cm. All horses start at their lowest point at the beginning of the ride. (a) Find angular acceleration a and initial angular speed wo of the carousel, and find the time at which the carousel reaches its maximum angular speed. (b) At t = 1.00 min, t = 2.00 min, and t = 3.00 min after the beginning of the ride, draw the velocity and acceleration vectors of a horse in the outer lane and a horse in the inner lane, with clearly labeled components. (If needed for clarity, you may draw both a top view and a side view.)

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Problem 5. Carousel that’s turning A carousel has two lanes of horses: an outer lane of radius 5.36 m and an inner lane of radius 3.78 m. When a ride starts, the carousel immediately starts rotating with some initial angular speed wo, and undergoes a constant angular acceleration a until it reaches its maximum angular speed, after which it rotates constantly at this angular speed. The carousel completes its first revolution in 23.0 s, then completes its second revolution after an additional 21.0s. At its maximum speed, the carousel completes one revolution every 14.0 s. During the ride, the horses also move up and down, and their vertical motion is independent of the angular speed of the carousel. The vertical displacement of each horse follows that of simple harmonic motion, with one up-and-down cycle lasting 3.50 s, and the height difference between each horse's highest point and lowest point being 20.3 cm. All horses start at their lowest point at the beginning of the ride. (a) Find angular acceleration a and initial angular speed wo of the carousel, and find the time at which the carousel reaches its maximum angular speed. (b) At t = 1.00 min, t = 2.00 min, and t = 3.00 min after the beginning of the ride, draw the velocity and acceleration vectors of a horse in the outer lane and a horse in the inner lane, with clearly labeled components. (If needed for clarity, you may draw both a top view and a side view.)
Transcribed Image Text:Problem 5. Carousel that’s turning A carousel has two lanes of horses: an outer lane of radius 5.36 m and an inner lane of radius 3.78 m. When a ride starts, the carousel immediately starts rotating with some initial angular speed wo, and undergoes a constant angular acceleration a until it reaches its maximum angular speed, after which it rotates constantly at this angular speed. The carousel completes its first revolution in 23.0 s, then completes its second revolution after an additional 21.0s. At its maximum speed, the carousel completes one revolution every 14.0 s. During the ride, the horses also move up and down, and their vertical motion is independent of the angular speed of the carousel. The vertical displacement of each horse follows that of simple harmonic motion, with one up-and-down cycle lasting 3.50 s, and the height difference between each horse's highest point and lowest point being 20.3 cm. All horses start at their lowest point at the beginning of the ride. (a) Find angular acceleration a and initial angular speed wo of the carousel, and find the time at which the carousel reaches its maximum angular speed. (b) At t = 1.00 min, t = 2.00 min, and t = 3.00 min after the beginning of the ride, draw the velocity and acceleration vectors of a horse in the outer lane and a horse in the inner lane, with clearly labeled components. (If needed for clarity, you may draw both a top view and a side view.)
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