A 1.3-kg model airplane flies in a circular path on the end of a 23-m line. The plane makes 4.3 revolutions each minute.

a. What is the period of the motion?

b. What is the speed of the plane?

c. What is the acceleration of the model plane?

d. How much force must the line exert on the plane to keep it moving in the circular

motion?

(a) The plane makes 4.3 revolutions per minute, so it makes a single revolution in

(1 min) / (4.3 rev) ≈ 0.2326 min ≈ 13.95 s ≈ 14 s

(b) The plane completes 1 revolution in about 14 s, so that in this time it travels a distance equal to the circumference of the path:

(2π (23 m)) / (14 s) ≈ 10.3568 m/s ≈ 10 m/s

(c) The plane accelerates toward the center of the path with magnitude

a = (10 m/s)² / (23 m) ≈ 4.6636 m/s² ≈ 4.7 m/s²

(d) By Newton's second law, the tension in the line is

F = (1.3 kg) (4.7 m/s²) ≈ 6.0627 N ≈ 6.1 N

a.   mass number from atomic number