Final answer:
a. It will take 9 seconds for the pulley to rotate 1/2 of a spin. b. The pulley will rotate 36 degrees in an hour. c. The pulley will rotate 108 degrees in 20 minutes.
Step-by-step explanation:
a. To find how long it will take for 1/2 of a spin, we need to determine the fraction of a full spin that 1/2 of a spin represents. Since a full spin is 360 degrees, 1/2 of a spin would be 1/2 * 360 degrees = 180 degrees. Since the pulley rotates 80 degrees every 4 seconds, we can set up a proportion to find the time it takes:
80 degrees / 4 seconds = 180 degrees / x seconds
Cross multiplying, we get:
80 * x = 4 * 180
Dividing both sides by 80:
x = (4 * 180) / 80
Simplifying, we get:
x = 9 seconds
Therefore, it will take 9 seconds for the pulley to rotate 1/2 of a spin.
b. To find how many degrees the pulley will rotate in an hour, we can start by finding how many seconds are in an hour. Since there are 60 seconds in a minute and 60 minutes in an hour, there are 60 * 60 = 3600 seconds in an hour. So, in 3600 seconds, the pulley rotates 360 degrees. Therefore, in 1 second, the pulley rotates 360 degrees / 3600 seconds = 0.1 degrees. Since there are 360 degrees in a full spin, the pulley will rotate 360 * 0.1 = 36 degrees in an hour.
c. To find how many degrees the pulley will rotate in 20 minutes, we can use the same approach as in part b. In 20 minutes, there are 20 * 60 = 1200 seconds. So, in 1200 seconds, the pulley rotates 360 degrees. Therefore, in 1 second, the pulley rotates 360 degrees / 1200 seconds = 0.3 degrees. Since there are 360 degrees in a full spin, the pulley will rotate 360 * 0.3 = 108 degrees in 20 minutes.