eduardo designs a toy with a rotary flywheel that rotates at a maximum speed of 170 revolutions per minute. suppose the flywheel is operating at its maximum speed for one minute and then the power supply to the toy is turned off. each subsequent minute thereafter, the flywheel rotates two-fifths as many times as in the preceding minute. how many complete revolutions will the flywheel make before coming to a stop?
In the first minute, the flywheel will make 170 revolutions.
In the second minute, the flywheel will make (2/5) * 170 = 68 revolutions.
In the third minute, the flywheel will make (2/5) * 68 = 27.2 revolutions. Since the flywheel can only make complete revolutions, we round this down to 27 revolutions.
In the fourth minute, the flywheel will make (2/5) * 27 = 10.8 revolutions. Rounded down, this is 10 revolutions.
In the fifth minute, the flywheel will make (2/5) * 10 = 4 revolutions.
After the fifth minute, the flywheel will no longer be rotating, since the number of revolutions will be less than 1.
Therefore, the total number of revolutions the flywheel will make before coming to a stop is:
170 + 68 + 27 + 10 + 4 = 279.
To find out the number of complete revolutions the flywheel will make before coming to a stop, we need to calculate the number of revolutions in each minute and sum them up.
Given:
Maximum speed of the flywheel = 170 revolutions per minute
Each subsequent minute, the flywheel rotates two-fifths as many times as in the preceding minute.
Let's calculate the number of revolutions for each minute:
1st minute: 170 revolutions (maximum speed)
2nd minute: (2/5) * 170 revolutions = 68 revolutions
3rd minute: (2/5) * 68 revolutions = 27.2 revolutions (approximated to 27 revolutions because we're looking for complete revolutions)
Now, we can sum up the number of revolutions for each minute:
170 + 68 + 27 = 265 revolutions
Therefore, the flywheel will make a total of 265 complete revolutions before coming to a stop.