The figure shown the chain drive of a bicycle. How far will the bicycle move if the pedals are rotated at 180°. Assume the radius of the bicycle wheel is 13.6 inches. There's a small circle w/a radius of 1.38 in and a large circle w/ 4.33 in.
Where I said "diameter" I meant circumference
assuming the pedal sprocket has a radius of 4.33 in
and the back wheel sprocket has the radius of 1.38 in
diameter of pedal wheel = 2π(4.33) = 27.20619
diameter of back wheel sprocket = 2π(1.38) = 8.670796
diameter of back wheel = 2π(13.6) = 85.45132
for each rotation of the pedal sprocket, the back wheel will rotate 27.20619/8.670796 times
= 3.13768 times
so it cover a distance of 3.13768 x 85.45132
= 268.119 inches.
or using a simple ratio ....
x/(2π(13.6)) = 2π(4.33)/(2π(1.38))
x = 2π(13.6)(4.33)/1.38
= above answer
but that is the distance covered for one complete rotation of the pedals
We want 180° or 1/2 a rotation, so the distance covered is
134.06 inches or 11 feet 2 inches
Well, that's quite a figure you've got there! It seems you have a chain drive, a small circle, and a large circle going on. Now, let's figure out how far this bicycle will move when the pedals are rotated at 180°.
Assuming that the radius of the bicycle wheel is 13.6 inches, we can use the formula for the circumference of a circle: circumference = 2 * π * radius.
For the small circle with a radius of 1.38 inches, the circumference would be 2 * π * 1.38 = 8.66 inches.
Now, for the large circle with a radius of 4.33 inches, the circumference would be 2 * π * 4.33 = 27.18 inches.
Since the chain connects these two circles, it means that when the small circle completes a full rotation of 360°, the large circle will move a distance equal to its circumference.
So, if the pedals are rotated at 180°, we can assume that the large circle will move half of its circumference.
Therefore, the bicycle will move half of 27.18 inches, which is approximately 13.59 inches.
So, when the pedals are rotated at 180°, the bicycle will move approximately 13.59 inches. Now, that's a chain reaction I can get behind!
To calculate the distance the bicycle will move if the pedals are rotated at 180°, we need to determine the circumference of the chain drive.
The chain drive consists of two circles: a small circle and a large circle.
Let's start with the small circle. The radius of the small circle is given as 1.38 inches. The circumference of a circle is calculated using the formula:
Circumference = 2 * π * radius
Therefore, the circumference of the small circle is:
Circumference of small circle = 2 * π * 1.38 inches
Now, let's move on to the large circle. The radius of the large circle is given as 4.33 inches. Again, we can calculate the circumference using the same formula:
Circumference = 2 * π * radius
Thus, the circumference of the large circle is:
Circumference of large circle = 2 * π * 4.33 inches
Since the bicycle is using a chain drive, the distance the bicycle will move is equal to the difference between the circumferences of the two circles. So, the distance the bicycle will move is:
Distance = Circumference of large circle - Circumference of small circle
Now we can substitute the values we calculated:
Distance = (2 * π * 4.33 inches) - (2 * π * 1.38 inches)
Simplifying further:
Distance = 8.66π inches - 2.76π inches
Distance = 5.9π inches (approximately)
Since the radius of the bicycle wheel is given as 13.6 inches, we can calculate the actual distance by multiplying the above result by the number of revolutions of the wheel:
Actual distance = Distance * Number of Wheel Revolutions
To calculate the number of revolutions, we need to know the gear ratio or the number of teeth on each gear. Without that information, we cannot provide an exact answer.
To determine how far the bicycle will move when the pedals are rotated at 180°, we need to calculate the circumference of the bicycle wheel.
The circumference of a circle can be calculated using the formula:
Circumference = 2 * π * Radius
In this case, the radius of the bicycle wheel is given as 13.6 inches. So, the circumference would be:
Circumference = 2 * π * 13.6
To find out how far the bicycle moves when the pedals are rotated at 180°, we have to calculate half of the circumference since a 180° rotation represents half a circle:
Distance moved = 0.5 * Circumference
Now, let's substitute the values into the equation and calculate the distance:
Circumference = 2 * 3.14 * 13.6
Circumference ≈ 2 * 3.14 * 13.6
Circumference ≈ 85.6 inches
Distance moved = 0.5 * 85.6
Distance moved ≈ 42.8 inches
Therefore, the bicycle will move approximately 42.8 inches when the pedals are rotated at 180°.