Question

The radius of each wheel on a bicycle is 0.400 m. the bicycle travels a distance of 3.0 km. assuming that the wheels do not slip, how many revolutions does each wheel make?

Answer 1

The wheels of the bicycle make approximately 1194 revolutions when traveling a distance of 3.0 km.

Step-by-step explanation:

To find how many revolutions each wheel makes, we need to first calculate the distance traveled by the bicycle. We know that the distance is 3.0 km and the radius of each wheel is 0.400 m. The circumference of each wheel can be found using the formula C = 2πr, where r is the radius. So, the circumference of each wheel is 2π(0.400) = 2.512 m.

To find the number of revolutions, we can use the formula N = d/C, where N is the number of revolutions, d is the distance traveled, and C is the circumference of each wheel. Plugging in the values, we get N = 3.0 km / 2.512 m = 1194.49 revolutions. Since we can't have fractional revolutions, each wheel would make approximately 1194 revolutions.

Answer 2

First, we need to calculate the perimeter of the wheel:

`p= 2 \pi r= 2 \pi (0.400 m)=2.51 m`
The perimeter corresponds to one complete revolution of the wheel. The wheel travels for a total of
`L=3.0 km=3000 m`, so in order to understand to how many revolutions does this number corresponds, we can set a simple proportion:

`2.51 m: 1 rev = 3000 m:x`
And so, we find

`x= (3000 m)/(2.51 m)=1195 rev`
So, each wheel made 1195 revolutions.