The figure shown the chain drive of a bicycle. How far will the bicycle move if the pedals are rotated at 120°. Assume the radius of the bicycle wheel is 10 inches.
no figure, but since arc length is s = rθ, the bike will travel
10 * 2π/3 inches
Well, let's see... If the pedals are rotated at 120°, I'm assuming you don't mean in a circle in the sky, right? That would be quite the spectacle!
Now, to calculate how far the bicycle will move, we need to figure out the distance covered by one revolution of the wheel. To do that, we can use the formula: distance = 2πr, where r is the radius of the wheel.
In this case, the radius of the bicycle wheel is given as 10 inches. So, plugging that into the formula, we get: distance = 2π(10) = 20π inches.
Now, since the distance covered is for one revolution of the wheel, we need to find out how many revolutions are covered when the pedals are rotated at 120°. A full revolution is 360°, so we can calculate the fraction of a revolution covered by 120° as: fraction = 120°/360° = 1/3.
Finally, to find out the total distance covered by the bicycle, we multiply the distance covered in one revolution by the fraction of a revolution covered. Therefore, the total distance covered by the bicycle is: total distance = 20π inches * (1/3) = (20π/3) inches.
So, the bicycle will move approximately (20π/3) inches when the pedals are rotated at 120°. Keep pedaling and enjoy the ride!
To find out how far the bicycle will move when the pedals are rotated at 120°, we need to calculate the circumference of the bicycle wheel and then find the distance traveled based on the angle of rotation.
1. Calculate the circumference of the bicycle wheel:
Circumference = 2 * π * radius
Given that the radius of the bicycle wheel is 10 inches, we can substitute the value and calculate the circumference:
Circumference = 2 * π * 10 inches
Hence, the circumference of the bicycle wheel is 20π inches (approximately 62.83 inches).
2. Determine the distance traveled based on the angle of rotation:
The angle of rotation is given as 120°, and we know that a complete revolution is 360°.
Let's calculate the percentage of the angle that corresponds to the distance traveled:
Percentage of distance traveled = Angle of rotation / 360°
Percentage of distance traveled = 120° / 360°
Percentage of distance traveled = 1/3
To find the distance traveled, multiply the percentage by the circumference of the wheel:
Distance traveled = Percentage of distance traveled * Circumference
Distance traveled = (1/3) * 20π
Distance traveled ≈ 20π/3 inches
Therefore, the bicycle will move approximately 20π/3 inches when the pedals are rotated at 120°.