You are riding a stationary exercise bike. Assume the rear wheel is twenty0eight inches in diameter,...

You are riding a stationary exercise bike. Assume the rear wheel is twenty0eight inches in diameter, the rear sprocket has a radius of two inches and the front sprocket has a radius of five inches. How many resolutions per minjute of the front sprocket produces a forward speed of forty milers per hour on the bike?

Expert Solution

Hey there!

Hope you are safe being in these Lockdown days.Now, let me answer this question for you.. First lets draw the diagram for what the question really asks for.

With the given question I have marked the radius in each circle. First let us find the circumference of each circles here. We know that the circumference of a circle is . By substituting the value of the radius 2 , 5 and 14 (diameter is 28 inches) in each circle , we get the values of their circumference as 12.56 inches , 31.42 inches and 87.97 inches.

Now by dividing the circumference of the sprocket of radius of 5 inches by the sprocket of radius 2 inches. we will know the number of rotations that the small sprocket spins when the bigger sprocket spins for 1 time.

That is 31.42 / 12.568 = 2.5 ROTATIONS IN SMALL SPROCKET WHEN THE BIGGER SPROCKET IS ROTATED FOR 1 TIME.

But the fact is that since the small sprocket is attached to the center of the wheel the number of rotations that the small sprocket spins is going to be the same number of rotation the wheel spins. In that case the wheel also spins 2.5 times when the bigger sprocket is spun for 1 time.

In that case when the bigger sprocket rotates for 1 time, the distance by covered by the wheel is 2.5 x (circumference of the wheel) = 2.5 x 87.97 = 220 inches

Well, let me give you an information of how much inches a mile is. It is 63360 inches in a mile.

In the question it talks about 40 miles per hour , and that means the wheel has to cover 40 miles , that is 40 x 63360 inches = 2534400 inches in an hour.

We already know that with one rotation of the bigger sprocket, the wheel covers 220 inches. In that case to cover 2534400 , the bigger sprocket has to rotate

I hope you get the idea. Cheers :)

genius_generous answered 2 years ago

The radius of the wheel on a bike is 27 inches. If the wheel is revolving...

The radius of the wheel on a bike is 27 inches. If the wheel is revolving at 144 revolutions per minute, what is the linear speed of the bike, in miles per hour? Round your answer to the nearest tenth, and do not include units in your answer.

A wheel on an indoor exercise bike (a spinning bike) accelerates steadily from 130 rpm to...

A wheel on an indoor exercise bike (a spinning bike) accelerates steadily from 130 rpm to 280 rpm in 5.0 s . The radius of the wheel is 47 cm. Determine the tangential component of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating.

Bob is at the Boston Biceps Bodybuilding Club riding an exercise bike. Bob wants to change...

Bob is at the Boston Biceps Bodybuilding Club riding an exercise bike. Bob wants to change the channel on the television that is mounted high on a nearby wall. He reaches for the remote control device and finds that another member has accidentally taken the remote control and left behind a cellular phone. Bob drags the exercise bike over to the television. He stands on the seat of the exercise bike in order to reach the television, but the seat...

You are riding on a Ferris wheel while standing on a scale. The scale normally reads...

You are riding on a Ferris wheel while standing on a scale. The scale normally reads 1500 lbs. (Did I mention you're a robot made of incredibly heavy metal?) While you are riding, you notice your weight on the scale changing. At the TOP of the Ferris wheel, you weigh only 1430 lbs. The Ferris wheel has a diameter of 230 m. How much time does it take the Ferris wheel to make one full turn? (Give answer in seconds).

1. You’re riding your bike in the bike lane through Golden Gate Park. Suddenly, you drift...

1. You’re riding your bike in the bike lane through Golden Gate Park. Suddenly, you drift out of the bike lane and into automobile traffic. Fortunately, you quickly move back into the bike lane and continue toward Ocean Beach. This scenario is a metaphor for homeostasis, where the controlled condition (physiologic variable) is the position of the bike on the road (e.g., inside or outside the bike lane). Identify: (a) The established set point for the controlled condition (b) The...

A bicycle wheel has a diameter of 63.0 cm and a mass of 1.74 kg. Assume...

A bicycle wheel has a diameter of 63.0 cm and a mass of 1.74 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 117 N is applied tangent to the rim of the tire. (a) What force must be applied by a chain passing over a 8.99-cm-diameter sprocket in order to give the wheel an acceleration of 4.49...

You are riding your bicycle directly away from a stationary source of sound and hear a...

You are riding your bicycle directly away from a stationary source of sound and hear a frequency that is 0.7% lower than the emitted frequency. The speed of sound is 346 m/s. What is your speed?

Assume that you have two cylindrical steel samples with 1 in diameter, one made out of...

Assume that you have two cylindrical steel samples with 1 in diameter, one made out of AISI 1045 and another one made out of AISI 4140. You austenitize and quench both samples in oil. Then you cut a section and measure the hardness at the center of each sample. Would you expect to get the same results? Explain your answer.

Exercise 1: Assume you have the following data about a country. Use the information and formulas...

Exercise 1: Assume you have the following data about a country. Use the information and formulas in chapter 9 and the chapter 9 study guide to fill in the table below. (Note: these are actual data, except the rate of economic growth. Rate of economic growth data are roughly US’s average from the past (3%) and China’s projected growth rate in the near future. Are these good assumptions to use?) USA China Nominal GDP 2019 (in millions of US$) 21,430,000...

A long position in a call option with an exercise price of $100. Assume that the call costs $10 when you purchase it.

A long position in a call option with an exercise price of $100. Assume that the call costs $10 when you purchase it.1B) If the stock price at expiration is $150, what is the likely value of the call option?1C) What is the maximum loss an investor would face on the call?

Question