A bicycle with tires 64 cm in diameter travels 5.2 km .
Part A
How many revolutions do the wheels make?
Express your answer using two significant figures.
r = .32 meter
c = 2 pi r
n = 5200 meters / (2 pi r meters)
To find the number of revolutions the wheels make, we need to determine the distance traveled by each revolution and then divide the total distance traveled by this value.
First, let's find the circumference of the bicycle wheel. The circumference can be calculated using the formula:
C = π × diameter
Given the diameter of the wheel is 64 cm, we can substitute it into the formula:
C = π × 64 cm
Using the approximation of π as 3.14, we can calculate the circumference:
C = 3.14 × 64 cm
C ≈ 201.6 cm
Next, we need to convert the distance traveled from kilometers to centimeters since the circumference is in centimeters. We can multiply the distance by 100,000 to convert it:
Distance in centimeters = 5.2 km × 100,000 cm/km
Distance in centimeters = 520,000 cm
Now, we can find the number of revolutions by dividing the distance traveled (in centimeters) by the circumference:
Number of revolutions = Distance in centimeters / Circumference
Number of revolutions = 520,000 cm / 201.6 cm
Calculating this expression gives us:
Number of revolutions ≈ 2579 revolutions
Therefore, the bicycle wheels make approximately 2579 revolutions when traveling 5.2 km.