Knowee
Questions
Features
Study Tools

The sprockets and chain of a bicycle are shown in the following figure.A chain of a bicycle goes around a pedal sprocket and a wheel sprocket.The radius of the pedal sprocket is 4 in.The radius of the wheel sprocket is 2 in.The radius of the back wheel of the bicycle is 13 in.The pedal sprocket has a radius of 4 in., the wheel sprocket a radius of 2 in., and the wheel a radius of 13 in. The cyclist pedals at 55 rpm.(a)Find the angular speed of the wheel sprocket (in rad/min). rad/min(b)Find the linear speed of the bicycle (in mi/h). (Assume that the wheel turns at the same rate as the wheel sprocket. Round your answer to one decimal place.) mi/h

Question

The sprockets and chain of a bicycle are shown in the following figure.A chain of a bicycle goes around a pedal sprocket and a wheel sprocket.The radius of the pedal sprocket is 4 in.The radius of the wheel sprocket is 2 in.The radius of the back wheel of the bicycle is 13 in.The pedal sprocket has a radius of 4 in., the wheel sprocket a radius of 2 in., and the wheel a radius of 13 in. The cyclist pedals at 55 rpm.(a)Find the angular speed of the wheel sprocket (in rad/min). rad/min(b)Find the linear speed of the bicycle (in mi/h). (Assume that the wheel turns at the same rate as the wheel sprocket. Round your answer to one decimal place.) mi/h

...expand
🧐 Not the exact question you are looking for?Go ask a question

Solution

(a) The angular speed of the wheel sprocket can be found by using the relationship between the pedal sprocket and the wheel sprocket. Since the radius of the pedal sprocket is twice that of the wheel sprocket, the wheel sprocket must rotate twice as fast for the chain to remain taut. Therefore, the angular speed of the wheel sprocket is 2 * 55 rpm = 110 rad/min.

(b) The linear speed of the bicycle can be found by using the relationship between the wheel sprocket and the wheel. Since the wheel sprocket and the wheel rotate at the same rate, the linear speed of the bicycle is the circumference of the wheel times the rotation rate of the wheel. The circumference of the wheel is 2 * pi * 13 in = 81.68 in. Therefore, the linear speed of the bicycle is 81.68 in/rev * 110 rev/min = 8984.8 in/min. To convert this to miles per hour, we use the conversion factors 1 mile = 63360 inches and 1 hour = 60 minutes. Therefore, the linear speed of the bicycle is (8984.8 in/min) * (1 mile/63360 in) * (60 min/1 hour) = 8.5 mi/h.

This problem has been solved

Similar Questions

The circumference of a bicycle wheel is 2 meters. If it rotates at 1 revolution per second then its linear speed is? Group of answer choices3 m/s3.14 m/s2 m/s6.28 m/s

A bicycle wheel has a diameter of 64.6 cm and a mass of 1.87 kg. Assume that the wheel is a hoop with all of its mass concentrated on the outside radius. The bicycle is placed on a stationary stand on rollers and a resistive force of 123 N is applied tangent to the rim of the tire.(a) What force must be applied by a chain passing over a 8.93 cm diameter sprocket if the wheel is to attain an acceleration of 4.60 rad/s2? N(b) What force is required if the chain shifts to a 5.55 cm diameter sprocket?

A bicycle is moving at 8.84 m/s. What is the angular speed of its tires if their radius is 35.5 cm?

Wheel of an engine rotates with an angular speed of 120 rev/min. If radius of the wheel is 2 m, then linear speed ofany point on its rim i

When you ride a bicycle, in what direction is the angular velocity of the wheels?(use your right hand to figure out the answer)Group of answer choicesto the leftto the rightforwardsbackwards PreviousNext

1/3

Upgrade your grade with Knowee

Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.