http://i.imgur.com/asLr4H2.png
It was an online homework assignment, that is a picture of the exact problem. I know that the linear speed formula is s/t (s being arc length and t being time). I was really unsure of how to execute this problem though.
I have tried executing this problem a few ways but can just not seem to grasp what to do. If someone can explain it to me step by step that would be great! Thanks!
It was an online homework assignment, that is a picture of the exact problem. I know that the linear speed formula is s/t (s being arc length and t being time). I was really unsure of how to execute this problem though.
I have tried executing this problem a few ways but can just not seem to grasp what to do. If someone can explain it to me step by step that would be great! Thanks!
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Find the linear speed of the bicycle in inches per minute,correct to two decimal places.
Ratio of Radius to RPM
The radii and the RPMs are inversely proportional.
5/3 = s/110
3s = 5 x 110
3s = 550
s = 550/3
s = 183.33 rpm Turning Rate of Rear Sprocket
The turning rate of the rear sprocket is the same as that of the rear wheel so…
ω = 183.33 rpm
Circumference of the Rear Wheel
C = circumference = to be determined
D = diameter = 19 inches
π = 3.14159
C = πD
C= (3.14159)(19 in.)
C = 59.69 inches
v = 183.33 revolutions/minute x 59.69 inches/revolution = 10,943.21 inches/minute ANSWER
How fast is the bike moving in miles per hour?
v = 10,943.21 inches/minute x 60 minutes/hour = 656,592.86 inches/hour
v = 656,592.86 inches/hour ÷ 12 inches/foot = 54,716.07 feet/hour
v = 54,716.07 feet/hour ÷ 5,280 feet/mile = 10.36 miles/hour ANSWER
Ratio of Radius to RPM
The radii and the RPMs are inversely proportional.
5/3 = s/110
3s = 5 x 110
3s = 550
s = 550/3
s = 183.33 rpm Turning Rate of Rear Sprocket
The turning rate of the rear sprocket is the same as that of the rear wheel so…
ω = 183.33 rpm
Circumference of the Rear Wheel
C = circumference = to be determined
D = diameter = 19 inches
π = 3.14159
C = πD
C= (3.14159)(19 in.)
C = 59.69 inches
v = 183.33 revolutions/minute x 59.69 inches/revolution = 10,943.21 inches/minute ANSWER
How fast is the bike moving in miles per hour?
v = 10,943.21 inches/minute x 60 minutes/hour = 656,592.86 inches/hour
v = 656,592.86 inches/hour ÷ 12 inches/foot = 54,716.07 feet/hour
v = 54,716.07 feet/hour ÷ 5,280 feet/mile = 10.36 miles/hour ANSWER
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All a chain does is extend the reach of the two sprockets. Any gears with teeth touching will have the same tangential velocity, or they would roll with the same linear speed on a flat surface. However, the rear sprocket and rear wheel are connected along the same axle. Any amount that the rear sprocket turns , the wheel will turn the same amount in degrees or radian. That means that the wheel and rear sprocket will always have the same angular velocity. Angular velocity is measured in angle per time or RPM (revolutions or 360 degrees per minute). The tangential speed of the wheel will equal the linear speed of the bike, because I assume there is no skidding. Just convert pedal speed in RPM to tangential speed which will be equal for both sprockets, then take that tangential speed and convet it angular speed using the small radius of the rear sprocket, then convert that angular speed into the final tangential speed using the larger wheel. Good luck!