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patelandrew816
29.07.2019 •
Mathematics
Consider a bicycle where the large central gear has a radius of 4 inches and the small back gear has a radius of 2 inches. how many inches would a point on the outer edge of the large gear travel in a 150º rotation? what degree of rotation will the small gear undergo when a point on its outer edge travels the same linear distance determined in part a? if the center of the small gear is rigidly attached to the center of a bicycle wheel with a radius of 10 inches, how many inches will the bicycle travel with a single rotation of the large gear? how does the distance you determined in part c change if the radius of the small gear is 1.5 inches and the radius of the large gear is 4.5 inches?
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Ответ:
Data:
large gear, R = 4 in
small gear, r = 2 in
Question 1.
Part A: How many inches would a point on the outer edge of the large gear travel in a 150º rotation?
Solution:
1) Circumferece of tthe large gear: 2πR = 2π(4in) = 8π in ≈ 25.13 in
2) 8π inches correspond to a full rotaion, i.e. 360°, so make a proportion to find the distance for 150° rotation:
8π x
= => x = (150°) * 8π / (360°) = 10.47 in
360° 150°
approximately 10.5 in.
Question 2:
Part B. What degree of rotation will the small gear undergo when a point on its outer edge travels the same linear distance determined in part A?
Solution:
1) A point on the outer edge of the small gear will translate (travel) the same linear distance determined in the part A.
2) Each full rotaion (360°) will travel 2π * 2 in = 4π in ≈ 12.57 in
3) So, make this proportion:
10.47 in 12.57
=
x 360°
And solve for x: x = 10.47 in * 360° / 12.57 in = 299.86°
practically 300°.
Question 3.
Part C. If the center of the small gear is rigidly attached to the center of a bicycle wheel with a radius of 10 inches, how many inches will the bicycle travel with a single rotation of the large gear?
Solution:
1) A full rotation of the small gear will make a full rotationof the bycicle wheel.
2) A full rotaion of the large gear will result in this number of rotations of the small gear:
1 rotation of large gear * 2π (4 in) = x * 2π (2 in)
=> x = (4 in / 2 in) = 2 rotaions
3) Each rotation of the small gear will lead to one full rotation of the wheel.
4) A full rotation of the wheel will lead to a translation equal to the circumference of the wheel, which is:
2π(radius) = 2π(10 in) = 62.83 in
Then, 2 rotation will be: 2 * 62.83 in = 125.66 in
about 125.66 in.
Question 4.
Part D) How does the distance you determined in part C change if the radius of the small gear is 1.5 inches and the radius of the large gear is 4.5 inches?
Solution:
1) one rotaion of the large gear => 2π (4.5 in) travel of a point on the outer edge
2) 2π(4.5 in) travel on the outer edge will translate into
2π(4.5 in) / 2π(1.5 in) = 4.5 / 1.5 = 3 rotations of the small gear
3) 3 rotations of the small gear = 3 rotations of the bycicle wheel
4) 3 rotations of the wheel => 3 * 2π(10 in) = 60 π ≈ 188.5 in
188.5 in
Ответ:
B
Step-by-step explanation:
As T is the midpoint of SU, ST=TU. 9x=5x+28, 4x=28, x=7. ST=TU=63 and SU=126