The large gear attached to the pedals connected to the smaller gear
attached to the wheel allows the bicycle to travel further per rotation.
Correct responses:
Part A: Approximately 10.47 inches
Part B: 300°The d
Part C: Approximately 125.66 inches
Part D: The distance traveled increases by approximately 62.83 inches
<h3 /><h3>Methods used to calculate the above values</h3>Given:
The radius of the large central gear, <em>r</em> = 4 inches
Radius of the small gear = 2 inches
Part A:
The distance travelled by the larger gear when the angle of rotation is 150° is given as follows;
Part B:
When the small gear travels the same linear distance as the large gear in part A, we have;
- The degree of rotation of the small gear = <u>300°</u>
Part C:
The distance travelled, <em>C</em>, by a single rotation of the large gear is given as follows;
C = 2 × π × 4 inches = 8·π inches
The degree of rotation of the smaller gear following one rotation of the large gear is therefore;
720° = 2 × 360°
1 complete rotation is equivalent to 360°.
Therefore'
720° is equivalent to two complete rotation.
Therefore, the smaller gear and the wheel rotates twice for each rotation of the large gear
The distance the bicycle travels = 2 × The circumference of the wheel
Therefore;
Distance traveled by the bicycle = 2 × 2 × π × 10 inches = 40·π inches
- Distance traveled by the bicycle = 40·π inches ≈ <u>125.66 inches</u>
Part D:
If the radius of the small gear is 1.5 inches and the radius of the large gear is 4.5 inches, we have;
Number of rotation of the small gear for each rotation of the large gear = 3 rotations
Therefore, number of rotation of the wheel = 3
Distance the bicycle travels = 3 × 2 × π × 10 inches = 60·π inches
The difference in distance traveled = 60·π inches - 40·π inches = 20·π inches
- The distance traveled by the bicycle increases by 20·π inches ≈ <u>62.83 inches</u>
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