A wheel 31.7 cm in diameter accelerates uniformly from 238 rpm to 347 rpm in 5.9 seconds. How far will a point on the rim of the wheel have travelled in this time?
To find the distance traveled by a point on the rim of the wheel, we need to calculate the total number of revolutions made by the wheel and then convert it to distance.
First, let's find the number of revolutions made by the wheel. We can calculate the change in revolutions per minute (RPM):
Change in RPM = Final RPM - Initial RPM
Change in RPM = 347 rpm - 238 rpm
Change in RPM = 109 rpm
Next, we need to convert this change in RPM to revolutions per second (RPS). Since there are 60 seconds in a minute, we can multiply the change in RPM by 1/60 to get the change in RPS:
Change in RPS = Change in RPM * (1/60)
Change in RPS = 109 rpm * (1/60)
Change in RPS = 1.8167 RPS (rounded to 4 decimal places)
Now, we can calculate the total number of revolutions made by the wheel in 5.9 seconds:
Total revolutions = Change in RPS * Time in seconds
Total revolutions = 1.8167 RPS * 5.9 s
Total revolutions = 10.7217 revolutions (rounded to 4 decimal places)
Since we know the diameter of the wheel, we can calculate the circumference using the formula:
Circumference = π * diameter
Circumference = 3.14159 * 31.7 cm
Circumference = 99.664053 cm (rounded to 6 decimal places)
To find the distance traveled by a point on the rim, we multiply the total number of revolutions by the circumference:
Distance = Total revolutions * Circumference
Distance = 10.7217 revolutions * 99.664053 cm
Distance = 1071.2097 cm (rounded to 4 decimal places)
Therefore, a point on the rim of the wheel will have traveled approximately 1071.2097 cm in 5.9 seconds.