# trigonometry

posted by .

The sprockets and chain of a bicycle are shown in the figure. 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 45 rpm.

(a) Find the angular speed of the wheel sprocket.

(b) Find the speed of the bicycle. (Assume that the wheel turns at the same rate as the wheel sprocket. Round your answer to one decimal place.)
mi/h

• trigonometry -

angular velocity:

Since circumference is linear and we are told the radius of the pedal sprocket is twice that of the wheel sprocket, for every turn of the pedal, the wheel will make 2 rotations
So in 1 minute the wheel turns 90 times
circumference of wheel = 2π(13) = 26π inches
distance covered in 1 minute = 90(26π) = 2340π inches

speed = 2340π inches/min
there are 12(5280) inches in 1 mile
and 60 minutes in 1 hour

speed = 2340π(60/(12(5280)) miles/hr
= appr 7.0 mph

• trigonometry -

kjekerj

## Similar Questions

1. ### physics

A bicycle chain is wrapped around a rear sprocket (r = 0.039m) and a front sprocket (r = 0.10m). The chain moves with a speed of 1.4m/s around the sprockets, while the bike moves at a constant velocity. Find the magnitude of the acceleration …
2. ### science

During a competition, a 60kg cyclist rides along a horizontal road on a bike with a mass of 5kg. During her ride, she changes gears and uses the chain wheel with a radius of 7.5cm and 36 teeth, and the rear sprocket with 18 teeth. …
3. ### physics

A bicycle wheel has a diameter of 64.2 cm and a mass of 1.79 kg. Assume that the wheel is a hoop with all of the mass concentrated on the outside radius. The bicycle is placed on a stationary stand and a resistive force of 115 N is …
4. ### Physics

A bicycle chain is wrapped around a rear sprocket (r = 0.038 m) and a front sprocket (r = 0.11 m). The chain moves with a speed of 1.6 m/s around the sprockets, while the bike moves at a constant velocity. Find the magnitude of the …
5. ### Physics

I am having trouble with the last portion of this question. If someone can help me, I would sincerely appreciate it. A bicycle wheel has a radius R = 32.0 cm and a mass M = 1.82 kg which you may assume to be concentrated on the outside …
6. ### Physics

I am having trouble with the last portion of this question. If someone can help me, I would sincerely appreciate it. A bicycle wheel has a radius R = 32.0 cm and a mass M = 1.82 kg which you may assume to be concentrated on the outside …
7. ### physics

A bicycle chain is wrapped around a rear sprocket (r = 0.041 m) and a front sprocket (r = 0.15 m). The chain moves with a speed of 1.4 m/s around the sprockets, while the bike moves at a constant velocity. Find the magnitude of the …
8. ### Trig

Jane has a bike with a 22-inch rear wheel. The wheel sprocket is 3 inches in diameter and the pedal sprocket is 4 inches in diameter (the sprockets hold the chain.) How fast in miles per hour is she going if she pedals at a rate of …
9. ### Pre-calc

A bicyclist is riding at 27 km/hour. She is pedaling at 95 rpm. Her rear wheel has radius 0.34 m and her rear sprocket has radius 0.03 m. A. What is the radius of her front sprocket?
10. ### Physics

a bicycle chain is wrapped around a rear sprocket (r=.039m) and a frond sprocket (r=0.10m) the chain moves with a speed of 1.4 m/s around the sprockets while the bike moves at a constant velocit find the madnitude of the acceleration …

More Similar Questions