Gears are important components in many mechanical devices, from mechanical clock

Question

Gears are important components in many mechanical devices, from mechanical clocks to bicycles. In fact, they are present whenever a motor produces rotational motion. An example of a simple gear system is shown in the figure (Figure 1) The bigger wheel (wheel 1) has radius r1, while the smaller one (wheel 2) has radius r2. The two wheels have small teeth and are connected through a metal chain so that when wheel 1 rotates, the chain moves with it and causes wheel 2 to rotate as well. A cyclist uses 27,000 joules per minute (this is about 385 food Calories per hour) to cycle at a constant pedaling rate of 450 radians per minute along a flat road using a gear ratio of 4. Find the torque rear exerted on the rear gear wheel. Express your answer in newton meters. When the cyclist encounters a steep hill, in order to maintain the same energy consumption and pedaling rate she changes her gear ratio to 0.7. Which of the following statements describes the change caused by the new gear ratio? The angular speed of the rear gear increases. The torque exerted on the rear gear wheel increases. The torque exerted on the front gear wheel increases. The power delivered to the rear gear wheel increases.

Explanation / Answer

work done = 27000 circuferece of the bigger wheel = 2*pi * r1 no of revolution = 450 rad/2 = 225 total distace = 225*2*pi*r1 = 450*pi*r work = F*S F = 27000/450*pi*r = 60/pi*r N Now rear wheel circumference = 2*pi*r2 distance = 250*2*pi*r2 = 450*pi*r2 r1 = 4r2 torque = r2 * 60/pi*r1 N = r2 * 60/pi*4r2 = 60/pi*4 = 15/pi Nm

Related Questions

Navigate

• Browse (All)
• Browse G
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.